# 最小頂點覆蓋基礎 · 脈衝 R06

本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。

本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。

batch-20261015-advance-20261115-r06-minimum-vertex-cover-foundations · 2026-10-15 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

[欄序與來源綁定資料](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], [[v0, v1], [v1, v2], [v2, v3]], [[v0, v2], [v1, v2], [v0, v1, v2], [v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 2, [[v0, v2], [v1, v2], [v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3], [[v0, v1], [v1, v2], [v2, v3]], [[v0, v2], [v1, v2], [v0, v1, v2], [v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 2, [[v0, v2], [v1, v2], [v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0001/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 2. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], [[v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 2, [[v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], [[v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 2, [[v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0002/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 3. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [[v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4], [v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 3, [[v0, v2, v4], [v1, v2, v4], [v1, v3, v4], [v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [[v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4], [v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 3, [[v0, v2, v4], [v1, v2, v4], [v1, v3, v4], [v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0003/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 4. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [[v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 3, [[v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [[v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 3, [[v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0004/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 5. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], [[v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 4, [[v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6], [v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], [[v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 4, [[v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6], [v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0005/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 6. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [[v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 4, [[v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [[v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 4, [[v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0006/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 7. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8], [v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8], [v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0007/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 8. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v1, v10, v3, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v1, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v1, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v1, v10, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v3, v5, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v1, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v3, v4, v5, v6, v7, v8], [v0, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v10, v2, v3, v5, v7, v9], [v1, v10, v2, v3, v5, v7, v9], [v0, v1, v10, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v0, v10, v2, v4, v5, v7, v9], [v1, v10, v2, v4, v5, v7, v9], [v0, v1, v10, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v1, v10, v3, v4, v5, v7, v9], [v0, v1, v10, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v10, v2, v3, v4, v5, v7, v9], [v1, v10, v2, v3, v4, v5, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v0, v10, v2, v4, v6, v7, v9], [v1, v10, v2, v4, v6, v7, v9], [v0, v1, v10, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v1, v10, v3, v4, v6, v7, v9], [v0, v1, v10, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v0, v10, v2, v3, v4, v6, v7, v9], [v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v1, v10, v3, v5, v6, v7, v9], [v0, v1, v10, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v10, v2, v3, v5, v6, v7, v9], [v1, v10, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v5, v6, v7, v9], [v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v1, v10, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v0, v10, v2, v4, v6, v8, v9], [v1, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v1, v10, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v1, v10, v3, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v1, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v1, v10, v3, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v1, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v1, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v1, v10, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v3, v5, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v1, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v3, v4, v5, v6, v7, v8], [v0, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v10, v2, v3, v5, v7, v9], [v1, v10, v2, v3, v5, v7, v9], [v0, v1, v10, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v0, v10, v2, v4, v5, v7, v9], [v1, v10, v2, v4, v5, v7, v9], [v0, v1, v10, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v1, v10, v3, v4, v5, v7, v9], [v0, v1, v10, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v10, v2, v3, v4, v5, v7, v9], [v1, v10, v2, v3, v4, v5, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v0, v10, v2, v4, v6, v7, v9], [v1, v10, v2, v4, v6, v7, v9], [v0, v1, v10, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v1, v10, v3, v4, v6, v7, v9], [v0, v1, v10, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v0, v10, v2, v3, v4, v6, v7, v9], [v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v1, v10, v3, v5, v6, v7, v9], [v0, v1, v10, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v10, v2, v3, v5, v6, v7, v9], [v1, v10, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v5, v6, v7, v9], [v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v1, v10, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v0, v10, v2, v4, v6, v8, v9], [v1, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v1, v10, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v1, v10, v3, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v1, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0008/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 9. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v0, v10, v11, v2, v4, v6, v8], [v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v11, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v1, v10, v11, v3, v4, v6, v8], [v0, v1, v10, v11, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v0, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v1, v10, v11, v3, v5, v6, v8], [v0, v1, v10, v11, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v11, v2, v3, v5, v6, v8], [v1, v10, v11, v2, v3, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v0, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v1, v10, v11, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v0, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v1, v10, v11, v3, v5, v7, v8], [v0, v1, v10, v11, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v11, v2, v3, v5, v7, v8], [v1, v10, v11, v2, v3, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, 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v2, v3, v5, v6, v8, v9], [v0, v11, v2, v3, v5, v6, v8, v9], [v1, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v0, v11, v2, v4, v5, v6, v8, v9], [v1, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v1, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v1, v11, v3, v5, v7, v8, v9], [v0, v1, v11, v3, v5, v7, v8, v9], [v1, v10, v11, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v11, v2, v3, v5, v7, v8, v9], [v1, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v0, v11, v2, v4, v5, v7, v8, v9], [v1, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v1, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v0, v11, v2, v4, v6, v7, v8, v9], [v1, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v1, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v1, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v1, v10, v3, v5, v7, v9], [v1, v11, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v0, v10, v11, v2, v4, v6, v8], [v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v11, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v1, v10, v11, v3, v4, v6, v8], [v0, v1, v10, v11, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v0, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v1, v10, v11, v3, v5, v6, v8], [v0, v1, v10, v11, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v11, v2, v3, v5, v6, v8], [v1, v10, v11, v2, v3, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v0, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v1, v10, v11, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v0, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v1, v10, v11, v3, v5, v7, v8], [v0, v1, v10, v11, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v11, v2, v3, v5, v7, v8], [v1, v10, v11, v2, v3, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v0, v10, v11, v2, v4, v5, v7, v8], [v1, v10, v11, v2, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v4, v5, v7, v8], [v1, v10, v3, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v1, v10, v11, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v1, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v11, v2, v3, v4, v5, v7, v8], [v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v1, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v0, v10, v11, v2, v4, v6, v7, v8], [v1, v10, v11, v2, v4, v6, v7, v8], [v0, v1, v10, v11, v2, v4, v6, v7, v8], [v1, v10, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v1, v10, v11, v3, v4, v6, v7, v8], [v0, v1, v10, v11, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], 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v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v1, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v1, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v1, v10, v3, v5, v7, v9], [v1, v11, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0009/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 10. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], [[v0, v1], [v0, v3], [v1, v2], [v2, v3]], [[v0, v2], [v0, v1, v2], [v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 2, [[v0, v2], [v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3], [[v0, v1], [v0, v3], [v1, v2], [v2, v3]], [[v0, v2], [v0, v1, v2], [v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 2, [[v0, v2], [v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0010/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 11. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], [[v0, v1], [v0, v4], [v1, v2], [v2, v3], [v3, v4]], [[v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 3, [[v0, v1, v3], [v0, v2, v3], [v0, v2, v4], [v1, v2, v4], [v1, v3, v4]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v0, v4], [v1, v2], [v2, v3], [v3, v4]], [[v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 3, [[v0, v1, v3], [v0, v2, v3], [v0, v2, v4], [v1, v2, v4], [v1, v3, v4]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0011/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 12. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v5], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [[v0, v2, v4], [v0, v1, v2, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 3, [[v0, v2, v4], [v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v5], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [[v0, v2, v4], [v0, v1, v2, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v1, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v1, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v1, v2, v4, v5], [v0, v1, v2, v4, v5], [v1, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 3, [[v0, v2, v4], [v1, v3, v5]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0012/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 13. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v6], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 4, [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v2, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v6], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v0, v1, v2, v4, v6], [v1, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v1, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v1, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v1, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v1, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v1, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 4, [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v2, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0013/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 14. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v0, v7], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], [[v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 4, [[v0, v2, v4, v6], [v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v0, v7], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], [[v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v1, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v1, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v1, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v1, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v1, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v1, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v1, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v1, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v1, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v1, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v1, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v1, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 4, [[v0, v2, v4, v6], [v1, v3, v5, v7]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0014/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 15. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 5, [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v1, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v1, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v1, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v1, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v1, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v1, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v1, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v1, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v1, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v1, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v1, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v1, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v1, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v1, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v1, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v1, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v1, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 5, [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0015/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 16. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v9], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v9], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8], [v1, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v1, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v1, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v1, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v1, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v1, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v1, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v1, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v1, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v1, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v1, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v1, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v1, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v1, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v1, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v1, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v1, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v1, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v1, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v1, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v1, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v1, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v1, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v1, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v1, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v1, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v1, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v1, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v1, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v1, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v1, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v1, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v1, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0016/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 17. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v10], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v1, v10, v3, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v1, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v1, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v1, v10, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v3, v5, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v1, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v3, v4, v5, v6, v7, v8], [v0, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v10, v2, v3, v5, v7, v9], [v1, v10, v2, v3, v5, v7, v9], [v0, v1, v10, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v0, v10, v2, v4, v5, v7, v9], [v1, v10, v2, v4, v5, v7, v9], [v0, v1, v10, v2, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v1, v10, v3, v4, v5, v7, v9], [v0, v1, v10, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v10, v2, v3, v4, v5, v7, v9], [v1, v10, v2, v3, v4, v5, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v0, v10, v2, v4, v6, v7, v9], [v1, v10, v2, v4, v6, v7, v9], [v0, v1, v10, v2, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v1, v10, v3, v4, v6, v7, v9], [v0, v1, v10, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v0, v10, v2, v3, v4, v6, v7, v9], [v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v1, v10, v3, v5, v6, v7, v9], [v0, v1, v10, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v10, v2, v3, v5, v6, v7, v9], [v1, v10, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v5, v6, v7, v9], [v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v1, v10, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v0, v10, v2, v4, v6, v8, v9], [v1, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v1, v10, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v1, v10, v3, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v1, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v2, v4, v6, v8, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v10], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v1, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v1, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v1, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v1, v10, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v10, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v1, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v1, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v1, v10, v3, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v1, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v1, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v1, v10, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v1, v10, v3, v5, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v1, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v4, v5, v6, v7, v8], [v1, v10, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v3, v4, v5, v6, v7, v8], [v0, v10, v2, v3, v4, v5, v6, v7, v8], [v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v10, v2, v3, v5, v7, v9], [v1, v10, v2, v3, v5, v7, v9], [v0, v1, v10, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v0, v10, v2, v4, v5, v7, v9], [v1, v10, v2, v4, v5, v7, v9], [v0, v1, v10, v2, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v1, v10, v3, v4, v5, v7, v9], [v0, v1, v10, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v10, v2, v3, v4, v5, v7, v9], [v1, v10, v2, v3, v4, v5, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v0, v10, v2, v4, v6, v7, v9], [v1, v10, v2, v4, v6, v7, v9], [v0, v1, v10, v2, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v1, v10, v3, v4, v6, v7, v9], [v0, v1, v10, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v0, v10, v2, v3, v4, v6, v7, v9], [v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v1, v10, v3, v5, v6, v7, v9], [v0, v1, v10, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v10, v2, v3, v5, v6, v7, v9], [v1, v10, v2, v3, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v5, v6, v7, v9], [v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v1, v10, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v0, v10, v2, v4, v6, v8, v9], [v1, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v1, v10, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v1, v10, v3, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v1, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v1, v10, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v1, v10, v3, v5, v7, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v1, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v1, v10, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v1, v10, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v1, v10, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v2, v4, v6, v8, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0017/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 18. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"],["v11","v0"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v11], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v0, v10, v11, v2, v4, v6, v8], [v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v1, v10, v11, v3, v4, v6, v8], [v0, v1, v10, v11, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v0, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v1, v10, v11, v3, v5, v6, v8], [v0, v1, v10, v11, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v11, v2, v3, v5, v6, v8], [v1, v10, v11, v2, v3, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v0, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v1, v10, v11, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v0, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v5, v7, v8], [v1, v10, v11, v3, v5, v7, v8], [v0, v1, v10, v11, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v11, v2, v3, v5, v7, v8], [v1, v10, v11, v2, v3, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v0, v10, v11, v2, v4, v5, v7, v8], [v1, v10, v11, v2, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v1, v10, v11, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v11, v2, v3, v4, v5, v7, v8], [v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v0, v10, v11, v2, v4, v6, v7, v8], [v1, v10, v11, v2, v4, v6, v7, v8], [v0, v1, v10, v11, v2, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v1, v10, v11, v3, v4, v6, v7, v8], [v0, v1, v10, v11, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v0, v10, v11, v2, v3, v4, v6, v7, v8], [v1, v10, v11, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v1, v10, v11, v3, v5, v6, v7, v8], [v0, v1, v10, v11, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v11, v2, v3, v5, v6, v7, v8], [v1, v10, v11, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, v2, 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v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v1, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v11, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v11], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], [[v0, v10, v2, v4, v6, v8], [v0, v1, v10, v2, v4, v6, v8], [v0, v10, v11, v2, v4, v6, v8], [v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v11, v2, v4, v6, v8], [v0, v1, v10, v3, v4, v6, v8], [v1, v10, v11, v3, v4, v6, v8], [v0, v1, v10, v11, v3, v4, v6, v8], [v0, v10, v2, v3, v4, v6, v8], [v0, v1, v10, v2, v3, v4, v6, v8], [v0, v10, v11, v2, v3, v4, v6, v8], [v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v8], [v0, v1, v10, v3, v5, v6, v8], [v1, v10, v11, v3, v5, v6, v8], [v0, v1, v10, v11, v3, v5, v6, v8], [v0, v10, v2, v3, v5, v6, v8], [v0, v1, v10, v2, v3, v5, v6, v8], [v0, v10, v11, v2, v3, v5, v6, v8], [v1, v10, v11, v2, v3, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v8], [v0, v10, v2, v4, v5, v6, v8], [v0, v1, v10, v2, v4, v5, v6, v8], [v0, v10, v11, v2, v4, v5, v6, v8], [v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v4, v5, v6, v8], [v0, v1, v10, v3, v4, v5, v6, v8], [v1, v10, v11, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v3, v4, v5, v6, v8], [v0, v10, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v2, v3, v4, v5, v6, v8], [v0, v10, v11, v2, v3, v4, v5, v6, v8], [v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8], [v0, v1, v10, v3, v5, v7, v8], [v1, v10, v11, v3, v5, v7, v8], [v0, v1, v10, v11, v3, v5, v7, v8], [v0, v10, v2, v3, v5, v7, v8], [v0, v1, v10, v2, v3, v5, v7, v8], [v0, v10, v11, v2, v3, v5, v7, v8], [v1, v10, v11, v2, v3, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v7, v8], [v0, v10, v2, v4, v5, v7, v8], [v0, v1, v10, v2, v4, v5, v7, v8], [v0, v10, v11, v2, v4, v5, v7, v8], [v1, v10, v11, v2, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v4, v5, v7, v8], [v0, v1, v10, v3, v4, v5, v7, v8], [v1, v10, v11, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v3, v4, v5, v7, v8], [v0, v10, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v2, v3, v4, v5, v7, v8], [v0, v10, v11, v2, v3, v4, v5, v7, v8], [v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8], [v0, v10, v2, v4, v6, v7, v8], [v0, v1, v10, v2, v4, v6, v7, v8], [v0, v10, v11, v2, v4, v6, v7, v8], [v1, v10, v11, v2, v4, v6, v7, v8], [v0, v1, v10, v11, v2, v4, v6, v7, v8], [v0, v1, v10, v3, v4, v6, v7, v8], [v1, v10, v11, v3, v4, v6, v7, v8], [v0, v1, v10, v11, v3, v4, v6, v7, v8], [v0, v10, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v2, v3, v4, v6, v7, v8], [v0, v10, v11, v2, v3, v4, v6, v7, v8], [v1, v10, v11, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8], [v0, v1, v10, v3, v5, v6, v7, v8], [v1, v10, v11, v3, v5, v6, v7, v8], [v0, v1, v10, v11, v3, v5, v6, v7, v8], [v0, v10, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v2, v3, v5, v6, v7, v8], [v0, v10, v11, v2, v3, v5, v6, v7, v8], [v1, v10, v11, v2, v3, v5, v6, v7, v8], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8], [v0, v10, v2, v4, v5, v6, v7, v8], [v0, v1, v10, 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v9], [v0, v11, v2, v4, v5, v6, v7, v9], [v1, v11, v2, v4, v5, v6, v7, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v9], [v1, v11, v3, v4, v5, v6, v7, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [v0, v10, v2, v4, v6, v8, v9], [v0, v1, v10, v2, v4, v6, v8, v9], [v0, v11, v2, v4, v6, v8, v9], [v1, v11, v2, v4, v6, v8, v9], [v0, v1, v11, v2, v4, v6, v8, v9], [v0, v10, v11, v2, v4, v6, v8, v9], [v1, v10, v11, v2, v4, v6, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v8, v9], [v0, v1, v10, v3, v4, v6, v8, v9], [v1, v11, v3, v4, v6, v8, v9], [v0, v1, v11, v3, v4, v6, v8, v9], [v1, v10, v11, v3, v4, v6, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v8, v9], [v0, v10, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v8, v9], [v0, v11, v2, v3, v4, v6, v8, v9], [v1, v11, v2, v3, v4, v6, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v8, v9], [v0, v1, v10, v3, v5, v6, v8, v9], [v1, v11, v3, v5, v6, v8, v9], [v0, v1, v11, v3, v5, v6, v8, v9], [v1, v10, v11, v3, v5, v6, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v8, v9], [v0, v10, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v8, v9], [v0, v11, v2, v3, v5, v6, v8, v9], [v1, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v8, v9], [v0, v10, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v8, v9], [v0, v11, v2, v4, v5, v6, v8, v9], [v1, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v8, v9], [v1, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v10, v3, v5, v7, v8, v9], [v1, v11, v3, v5, v7, v8, v9], [v0, v1, v11, v3, v5, v7, v8, v9], [v1, v10, v11, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v7, v8, v9], [v0, v10, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v7, v8, v9], [v0, v11, v2, v3, v5, v7, v8, v9], [v1, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v7, v8, v9], [v0, v10, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v7, v8, v9], [v0, v11, v2, v4, v5, v7, v8, v9], [v1, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v7, v8, v9], [v1, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v7, v8, v9], [v0, v10, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v6, v7, v8, v9], [v0, v11, v2, v4, v6, v7, v8, v9], [v1, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v6, v7, v8, v9], [v1, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v10, v3, v5, v6, v7, v8, v9], [v1, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v5, v6, v7, v8, v9], [v0, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v11, v3, v5, v7, v9]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0018/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 19. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], [[v0, v1], [v0, v2], [v0, v3]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3], [[v0, v1], [v0, v2], [v0, v3]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0019/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 20. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], [[v0, v1], [v0, v2], [v0, v3], [v0, v4]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v0, v2], [v0, v3], [v0, v4]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0020/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 21. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0021/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 22. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v1, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0022/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 23. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v0, v7], [v0, v1, v7], [v0, v2, v7], [v0, v1, v2, v7], [v0, v3, v7], [v0, v1, v3, v7], [v0, v2, v3, v7], [v0, v1, v2, v3, v7], [v0, v4, v7], [v0, v1, v4, v7], [v0, v2, v4, v7], [v0, v1, v2, v4, v7], [v0, v3, v4, v7], [v0, v1, v3, v4, v7], [v0, v2, v3, v4, v7], [v0, v1, v2, v3, v4, v7], [v0, v5, v7], [v0, v1, v5, v7], [v0, v2, v5, v7], [v0, v1, v2, v5, v7], [v0, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v4, v5, v7], [v0, v1, v4, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v6, v7], [v0, v1, v6, v7], [v0, v2, v6, v7], [v0, v1, v2, v6, v7], [v0, v3, v6, v7], [v0, v1, v3, v6, v7], [v0, v2, v3, v6, v7], [v0, v1, v2, v3, v6, v7], [v0, v4, v6, v7], [v0, v1, v4, v6, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v5, v6, v7], [v0, v1, v5, v6, v7], [v0, v2, v5, v6, v7], [v0, v1, v2, v5, v6, v7], [v0, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v4, v5, v6, v7], [v0, v1, v4, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v0, v7], [v0, v1, v7], [v0, v2, v7], [v0, v1, v2, v7], [v0, v3, v7], [v0, v1, v3, v7], [v0, v2, v3, v7], [v0, v1, v2, v3, v7], [v0, v4, v7], [v0, v1, v4, v7], [v0, v2, v4, v7], [v0, v1, v2, v4, v7], [v0, v3, v4, v7], [v0, v1, v3, v4, v7], [v0, v2, v3, v4, v7], [v0, v1, v2, v3, v4, v7], [v0, v5, v7], [v0, v1, v5, v7], [v0, v2, v5, v7], [v0, v1, v2, v5, v7], [v0, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v4, v5, v7], [v0, v1, v4, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v6, v7], [v0, v1, v6, v7], [v0, v2, v6, v7], [v0, v1, v2, v6, v7], [v0, v3, v6, v7], [v0, v1, v3, v6, v7], [v0, v2, v3, v6, v7], [v0, v1, v2, v3, v6, v7], [v0, v4, v6, v7], [v0, v1, v4, v6, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v5, v6, v7], [v0, v1, v5, v6, v7], [v0, v2, v5, v6, v7], [v0, v1, v2, v5, v6, v7], [v0, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v4, v5, v6, v7], [v0, v1, v4, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v1, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0023/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 24. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"],["v0","v8"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7], [v0, v8]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v0, v7], [v0, v1, v7], [v0, v2, v7], [v0, v1, v2, v7], [v0, v3, v7], [v0, v1, v3, v7], [v0, v2, v3, v7], [v0, v1, v2, v3, v7], [v0, v4, v7], [v0, v1, v4, v7], [v0, v2, v4, v7], [v0, v1, v2, v4, v7], [v0, v3, v4, v7], [v0, v1, v3, v4, v7], [v0, v2, v3, v4, v7], [v0, v1, v2, v3, v4, v7], [v0, v5, v7], [v0, v1, v5, v7], [v0, v2, v5, v7], [v0, v1, v2, v5, v7], [v0, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v4, v5, v7], [v0, v1, v4, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v6, v7], [v0, v1, v6, v7], [v0, v2, v6, v7], [v0, v1, v2, v6, v7], [v0, v3, v6, v7], [v0, v1, v3, v6, v7], [v0, v2, v3, v6, v7], [v0, v1, v2, v3, v6, v7], [v0, v4, v6, v7], [v0, v1, v4, v6, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v5, v6, v7], [v0, v1, v5, v6, v7], [v0, v2, v5, v6, v7], [v0, v1, v2, v5, v6, v7], [v0, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v4, v5, v6, v7], [v0, v1, v4, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v8], [v0, v1, v8], [v0, v2, v8], [v0, v1, v2, v8], [v0, v3, v8], [v0, v1, v3, v8], [v0, v2, v3, v8], [v0, v1, v2, v3, v8], [v0, v4, v8], [v0, v1, v4, v8], [v0, v2, v4, v8], [v0, v1, v2, v4, v8], [v0, v3, v4, v8], [v0, v1, v3, v4, v8], [v0, v2, v3, v4, v8], [v0, v1, v2, v3, v4, v8], [v0, v5, v8], [v0, v1, v5, v8], [v0, v2, v5, v8], [v0, v1, v2, v5, v8], [v0, v3, v5, v8], [v0, v1, v3, v5, v8], [v0, v2, v3, v5, v8], [v0, v1, v2, v3, v5, v8], [v0, v4, v5, v8], [v0, v1, v4, v5, v8], [v0, v2, v4, v5, v8], [v0, v1, v2, v4, v5, v8], [v0, v3, v4, v5, v8], [v0, v1, v3, v4, v5, v8], [v0, v2, v3, v4, v5, v8], [v0, v1, v2, v3, v4, v5, v8], [v0, v6, v8], [v0, v1, v6, v8], [v0, v2, v6, v8], [v0, v1, v2, v6, v8], [v0, v3, v6, v8], [v0, v1, v3, v6, v8], [v0, v2, v3, v6, v8], [v0, v1, v2, v3, v6, v8], [v0, v4, v6, v8], [v0, v1, v4, v6, v8], [v0, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v0, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v0, v5, v6, v8], [v0, v1, v5, v6, v8], [v0, v2, v5, v6, v8], [v0, v1, v2, v5, v6, v8], [v0, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v4, v5, v6, v8], [v0, v1, v4, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v0, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v0, v7, v8], [v0, v1, v7, v8], [v0, v2, v7, v8], [v0, v1, v2, v7, v8], [v0, v3, v7, v8], [v0, v1, v3, v7, v8], [v0, v2, v3, v7, v8], [v0, v1, v2, v3, v7, v8], [v0, v4, v7, v8], [v0, v1, v4, v7, v8], [v0, v2, v4, v7, v8], [v0, v1, v2, v4, v7, v8], [v0, v3, v4, v7, v8], [v0, v1, v3, v4, v7, v8], [v0, v2, v3, v4, v7, v8], [v0, v1, v2, v3, v4, v7, v8], [v0, v5, v7, v8], [v0, v1, v5, v7, v8], [v0, v2, v5, v7, v8], [v0, v1, v2, v5, v7, v8], [v0, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v4, v5, v7, v8], [v0, v1, v4, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v0, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v6, v7, v8], [v0, v1, v6, v7, v8], [v0, v2, v6, v7, v8], [v0, v1, v2, v6, v7, v8], [v0, v3, v6, v7, v8], [v0, v1, v3, v6, v7, v8], [v0, v2, v3, v6, v7, v8], [v0, v1, v2, v3, v6, v7, v8], [v0, v4, v6, v7, v8], [v0, v1, v4, v6, v7, v8], [v0, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v0, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v0, v5, v6, v7, v8], [v0, v1, v5, v6, v7, v8], [v0, v2, v5, v6, v7, v8], [v0, v1, v2, v5, v6, v7, v8], [v0, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v4, v5, v6, v7, v8], [v0, v1, v4, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v0, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7], [v0, v8]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v0, v7], [v0, v1, v7], [v0, v2, v7], [v0, v1, v2, v7], [v0, v3, v7], [v0, v1, v3, v7], [v0, v2, v3, v7], [v0, v1, v2, v3, v7], [v0, v4, v7], [v0, v1, v4, v7], [v0, v2, v4, v7], [v0, v1, v2, v4, v7], [v0, v3, v4, v7], [v0, v1, v3, v4, v7], [v0, v2, v3, v4, v7], [v0, v1, v2, v3, v4, v7], [v0, v5, v7], [v0, v1, v5, v7], [v0, v2, v5, v7], [v0, v1, v2, v5, v7], [v0, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v4, v5, v7], [v0, v1, v4, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v6, v7], [v0, v1, v6, v7], [v0, v2, v6, v7], [v0, v1, v2, v6, v7], [v0, v3, v6, v7], [v0, v1, v3, v6, v7], [v0, v2, v3, v6, v7], [v0, v1, v2, v3, v6, v7], [v0, v4, v6, v7], [v0, v1, v4, v6, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v5, v6, v7], [v0, v1, v5, v6, v7], [v0, v2, v5, v6, v7], [v0, v1, v2, v5, v6, v7], [v0, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v4, v5, v6, v7], [v0, v1, v4, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v8], [v0, v1, v8], [v0, v2, v8], [v0, v1, v2, v8], [v0, v3, v8], [v0, v1, v3, v8], [v0, v2, v3, v8], [v0, v1, v2, v3, v8], [v0, v4, v8], [v0, v1, v4, v8], [v0, v2, v4, v8], [v0, v1, v2, v4, v8], [v0, v3, v4, v8], [v0, v1, v3, v4, v8], [v0, v2, v3, v4, v8], [v0, v1, v2, v3, v4, v8], [v0, v5, v8], [v0, v1, v5, v8], [v0, v2, v5, v8], [v0, v1, v2, v5, v8], [v0, v3, v5, v8], [v0, v1, v3, v5, v8], [v0, v2, v3, v5, v8], [v0, v1, v2, v3, v5, v8], [v0, v4, v5, v8], [v0, v1, v4, v5, v8], [v0, v2, v4, v5, v8], [v0, v1, v2, v4, v5, v8], [v0, v3, v4, v5, v8], [v0, v1, v3, v4, v5, v8], [v0, v2, v3, v4, v5, v8], [v0, v1, v2, v3, v4, v5, v8], [v0, v6, v8], [v0, v1, v6, v8], [v0, v2, v6, v8], [v0, v1, v2, v6, v8], [v0, v3, v6, v8], [v0, v1, v3, v6, v8], [v0, v2, v3, v6, v8], [v0, v1, v2, v3, v6, v8], [v0, v4, v6, v8], [v0, v1, v4, v6, v8], [v0, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v0, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v0, v5, v6, v8], [v0, v1, v5, v6, v8], [v0, v2, v5, v6, v8], [v0, v1, v2, v5, v6, v8], [v0, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v4, v5, v6, v8], [v0, v1, v4, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v0, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v0, v7, v8], [v0, v1, v7, v8], [v0, v2, v7, v8], [v0, v1, v2, v7, v8], [v0, v3, v7, v8], [v0, v1, v3, v7, v8], [v0, v2, v3, v7, v8], [v0, v1, v2, v3, v7, v8], [v0, v4, v7, v8], [v0, v1, v4, v7, v8], [v0, v2, v4, v7, v8], [v0, v1, v2, v4, v7, v8], [v0, v3, v4, v7, v8], [v0, v1, v3, v4, v7, v8], [v0, v2, v3, v4, v7, v8], [v0, v1, v2, v3, v4, v7, v8], [v0, v5, v7, v8], [v0, v1, v5, v7, v8], [v0, v2, v5, v7, v8], [v0, v1, v2, v5, v7, v8], [v0, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v4, v5, v7, v8], [v0, v1, v4, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v0, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v6, v7, v8], [v0, v1, v6, v7, v8], [v0, v2, v6, v7, v8], [v0, v1, v2, v6, v7, v8], [v0, v3, v6, v7, v8], [v0, v1, v3, v6, v7, v8], [v0, v2, v3, v6, v7, v8], [v0, v1, v2, v3, v6, v7, v8], [v0, v4, v6, v7, v8], [v0, v1, v4, v6, v7, v8], [v0, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v0, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v0, v5, v6, v7, v8], [v0, v1, v5, v6, v7, v8], [v0, v2, v5, v6, v7, v8], [v0, v1, v2, v5, v6, v7, v8], [v0, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v4, v5, v6, v7, v8], [v0, v1, v4, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v0, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v1, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0024/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 25. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"],["v0","v8"],["v0","v9"]]}。請依 [vertices, edges, all_covers, minimum_size, minimum_covers, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7], [v0, v8], [v0, v9]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], [v0, v1, v2, v5, v6], [v0, v3, v5, v6], [v0, v1, v3, v5, v6], [v0, v2, v3, v5, v6], [v0, v1, v2, v3, v5, v6], [v0, v4, v5, v6], [v0, v1, v4, v5, v6], [v0, v2, v4, v5, v6], [v0, v1, v2, v4, v5, v6], [v0, v3, v4, v5, v6], [v0, v1, v3, v4, v5, v6], [v0, v2, v3, v4, v5, v6], [v0, v1, v2, v3, v4, v5, v6], [v0, v7], [v0, v1, v7], [v0, v2, v7], [v0, v1, v2, v7], [v0, v3, v7], [v0, v1, v3, v7], [v0, v2, v3, v7], [v0, v1, v2, v3, v7], [v0, v4, v7], [v0, v1, v4, v7], [v0, v2, v4, v7], [v0, v1, v2, v4, v7], [v0, v3, v4, v7], [v0, v1, v3, v4, v7], [v0, v2, v3, v4, v7], [v0, v1, v2, v3, v4, v7], [v0, v5, v7], [v0, v1, v5, v7], [v0, v2, v5, v7], [v0, v1, v2, v5, v7], [v0, v3, v5, v7], [v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v1, v2, v3, v5, v7], [v0, v4, v5, v7], [v0, v1, v4, v5, v7], [v0, v2, v4, v5, v7], [v0, v1, v2, v4, v5, v7], [v0, v3, v4, v5, v7], [v0, v1, v3, v4, v5, v7], [v0, v2, v3, v4, v5, v7], [v0, v1, v2, v3, v4, v5, v7], [v0, v6, v7], [v0, v1, v6, v7], [v0, v2, v6, v7], [v0, v1, v2, v6, v7], [v0, v3, v6, v7], [v0, v1, v3, v6, v7], [v0, v2, v3, v6, v7], [v0, v1, v2, v3, v6, v7], [v0, v4, v6, v7], [v0, v1, v4, v6, v7], [v0, v2, v4, v6, v7], [v0, v1, v2, v4, v6, v7], [v0, v3, v4, v6, v7], [v0, v1, v3, v4, v6, v7], [v0, v2, v3, v4, v6, v7], [v0, v1, v2, v3, v4, v6, v7], [v0, v5, v6, v7], [v0, v1, v5, v6, v7], [v0, v2, v5, v6, v7], [v0, v1, v2, v5, v6, v7], [v0, v3, v5, v6, v7], [v0, v1, v3, v5, v6, v7], [v0, v2, v3, v5, v6, v7], [v0, v1, v2, v3, v5, v6, v7], [v0, v4, v5, v6, v7], [v0, v1, v4, v5, v6, v7], [v0, v2, v4, v5, v6, v7], [v0, v1, v2, v4, v5, v6, v7], [v0, v3, v4, v5, v6, v7], [v0, v1, v3, v4, v5, v6, v7], [v0, v2, v3, v4, v5, v6, v7], [v0, v1, v2, v3, v4, v5, v6, v7], [v0, v8], [v0, v1, v8], [v0, v2, v8], [v0, v1, v2, v8], [v0, v3, v8], [v0, v1, v3, v8], [v0, v2, v3, v8], [v0, v1, v2, v3, v8], [v0, v4, v8], [v0, v1, v4, v8], [v0, v2, v4, v8], [v0, v1, v2, v4, v8], [v0, v3, v4, v8], [v0, v1, v3, v4, v8], [v0, v2, v3, v4, v8], [v0, v1, v2, v3, v4, v8], [v0, v5, v8], [v0, v1, v5, v8], [v0, v2, v5, v8], [v0, v1, v2, v5, v8], [v0, v3, v5, v8], [v0, v1, v3, v5, v8], [v0, v2, v3, v5, v8], [v0, v1, v2, v3, v5, v8], [v0, v4, v5, v8], [v0, v1, v4, v5, v8], [v0, v2, v4, v5, v8], [v0, v1, v2, v4, v5, v8], [v0, v3, v4, v5, v8], [v0, v1, v3, v4, v5, v8], [v0, v2, v3, v4, v5, v8], [v0, v1, v2, v3, v4, v5, v8], [v0, v6, v8], [v0, v1, v6, v8], [v0, v2, v6, v8], [v0, v1, v2, v6, v8], [v0, v3, v6, v8], [v0, v1, v3, v6, v8], [v0, v2, v3, v6, v8], [v0, v1, v2, v3, v6, v8], [v0, v4, v6, v8], [v0, v1, v4, v6, v8], [v0, v2, v4, v6, v8], [v0, v1, v2, v4, v6, v8], [v0, v3, v4, v6, v8], [v0, v1, v3, v4, v6, v8], [v0, v2, v3, v4, v6, v8], [v0, v1, v2, v3, v4, v6, v8], [v0, v5, v6, v8], [v0, v1, v5, v6, v8], [v0, v2, v5, v6, v8], [v0, v1, v2, v5, v6, v8], [v0, v3, v5, v6, v8], [v0, v1, v3, v5, v6, v8], [v0, v2, v3, v5, v6, v8], [v0, v1, v2, v3, v5, v6, v8], [v0, v4, v5, v6, v8], [v0, v1, v4, v5, v6, v8], [v0, v2, v4, v5, v6, v8], [v0, v1, v2, v4, v5, v6, v8], [v0, v3, v4, v5, v6, v8], [v0, v1, v3, v4, v5, v6, v8], [v0, v2, v3, v4, v5, v6, v8], [v0, v1, v2, v3, v4, v5, v6, v8], [v0, v7, v8], [v0, v1, v7, v8], [v0, v2, v7, v8], [v0, v1, v2, v7, v8], [v0, v3, v7, v8], [v0, v1, v3, v7, v8], [v0, v2, v3, v7, v8], [v0, v1, v2, v3, v7, v8], [v0, v4, v7, v8], [v0, v1, v4, v7, v8], [v0, v2, v4, v7, v8], [v0, v1, v2, v4, v7, v8], [v0, v3, v4, v7, v8], [v0, v1, v3, v4, v7, v8], [v0, v2, v3, v4, v7, v8], [v0, v1, v2, v3, v4, v7, v8], [v0, v5, v7, v8], [v0, v1, v5, v7, v8], [v0, v2, v5, v7, v8], [v0, v1, v2, v5, v7, v8], [v0, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v8], [v0, v2, v3, v5, v7, v8], [v0, v1, v2, v3, v5, v7, v8], [v0, v4, v5, v7, v8], [v0, v1, v4, v5, v7, v8], [v0, v2, v4, v5, v7, v8], [v0, v1, v2, v4, v5, v7, v8], [v0, v3, v4, v5, v7, v8], [v0, v1, v3, v4, v5, v7, v8], [v0, v2, v3, v4, v5, v7, v8], [v0, v1, v2, v3, v4, v5, v7, v8], [v0, v6, v7, v8], [v0, v1, v6, v7, v8], [v0, v2, v6, v7, v8], [v0, v1, v2, v6, v7, v8], [v0, v3, v6, v7, v8], [v0, v1, v3, v6, v7, v8], [v0, v2, v3, v6, v7, v8], [v0, v1, v2, v3, v6, v7, v8], [v0, v4, v6, v7, v8], [v0, v1, v4, v6, v7, v8], [v0, v2, v4, v6, v7, v8], [v0, v1, v2, v4, v6, v7, v8], [v0, v3, v4, v6, v7, v8], [v0, v1, v3, v4, v6, v7, v8], [v0, v2, v3, v4, v6, v7, v8], [v0, v1, v2, v3, v4, v6, v7, v8], [v0, v5, v6, v7, v8], [v0, v1, v5, v6, v7, v8], [v0, v2, v5, v6, v7, v8], [v0, v1, v2, v5, v6, v7, v8], [v0, v3, v5, v6, v7, v8], [v0, v1, v3, v5, v6, v7, v8], [v0, v2, v3, v5, v6, v7, v8], [v0, v1, v2, v3, v5, v6, v7, v8], [v0, v4, v5, v6, v7, v8], [v0, v1, v4, v5, v6, v7, v8], [v0, v2, v4, v5, v6, v7, v8], [v0, v1, v2, v4, v5, v6, v7, v8], [v0, v3, v4, v5, v6, v7, v8], [v0, v1, v3, v4, v5, v6, v7, v8], [v0, v2, v3, v4, v5, v6, v7, v8], [v0, v1, v2, v3, v4, v5, v6, v7, v8], [v0, v9], [v0, v1, v9], [v0, v2, v9], [v0, v1, v2, v9], [v0, v3, v9], [v0, v1, v3, v9], [v0, v2, v3, v9], [v0, v1, v2, v3, v9], [v0, v4, v9], [v0, v1, v4, v9], [v0, v2, v4, v9], [v0, v1, v2, v4, v9], [v0, v3, v4, v9], [v0, v1, v3, v4, v9], [v0, v2, v3, v4, v9], [v0, v1, v2, v3, v4, v9], [v0, v5, v9], [v0, v1, v5, v9], [v0, v2, v5, v9], [v0, v1, v2, v5, v9], [v0, v3, v5, v9], [v0, v1, v3, v5, v9], [v0, v2, v3, v5, v9], [v0, v1, v2, v3, v5, v9], [v0, v4, v5, v9], [v0, v1, v4, v5, v9], [v0, v2, v4, v5, v9], [v0, v1, v2, v4, v5, v9], [v0, v3, v4, v5, v9], [v0, v1, v3, v4, v5, v9], [v0, v2, v3, v4, v5, v9], [v0, v1, v2, v3, v4, v5, v9], [v0, v6, v9], [v0, v1, v6, v9], [v0, v2, v6, v9], [v0, v1, v2, v6, v9], [v0, v3, v6, v9], [v0, v1, v3, v6, v9], [v0, v2, v3, v6, v9], [v0, v1, v2, v3, v6, v9], [v0, v4, v6, v9], [v0, v1, v4, v6, v9], [v0, v2, v4, v6, v9], [v0, v1, v2, v4, v6, v9], [v0, v3, v4, v6, v9], [v0, v1, v3, v4, v6, v9], [v0, v2, v3, v4, v6, v9], [v0, v1, v2, v3, v4, v6, v9], [v0, v5, v6, v9], [v0, v1, v5, v6, v9], [v0, v2, v5, v6, v9], [v0, v1, v2, v5, v6, v9], [v0, v3, v5, v6, v9], [v0, v1, v3, v5, v6, v9], [v0, v2, v3, v5, v6, v9], [v0, v1, v2, v3, v5, v6, v9], [v0, v4, v5, v6, v9], [v0, v1, v4, v5, v6, v9], [v0, v2, v4, v5, v6, v9], [v0, v1, v2, v4, v5, v6, v9], [v0, v3, v4, v5, v6, v9], [v0, v1, v3, v4, v5, v6, v9], [v0, v2, v3, v4, v5, v6, v9], [v0, v1, v2, v3, v4, v5, v6, v9], [v0, v7, v9], [v0, v1, v7, v9], [v0, v2, v7, v9], [v0, v1, v2, v7, v9], [v0, v3, v7, v9], [v0, v1, v3, v7, v9], [v0, v2, v3, v7, v9], [v0, v1, v2, v3, v7, v9], [v0, v4, v7, v9], [v0, v1, v4, v7, v9], [v0, v2, v4, v7, v9], [v0, v1, v2, v4, v7, v9], [v0, v3, v4, v7, v9], [v0, v1, v3, v4, v7, v9], [v0, v2, v3, v4, v7, v9], [v0, v1, v2, v3, v4, v7, v9], [v0, v5, v7, v9], [v0, v1, v5, v7, v9], [v0, v2, v5, v7, v9], [v0, v1, v2, v5, v7, v9], [v0, v3, v5, v7, v9], [v0, v1, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v1, v2, v3, v5, v7, v9], [v0, v4, v5, v7, v9], [v0, v1, v4, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v1, v2, v4, v5, v7, v9], [v0, v3, v4, v5, v7, v9], [v0, v1, v3, v4, v5, v7, v9], [v0, v2, v3, v4, v5, v7, v9], [v0, v1, v2, v3, v4, v5, v7, v9], [v0, v6, v7, v9], [v0, v1, v6, v7, v9], [v0, v2, v6, v7, v9], [v0, v1, v2, v6, v7, v9], [v0, v3, v6, v7, v9], [v0, v1, v3, v6, v7, v9], [v0, v2, v3, v6, v7, v9], [v0, v1, v2, v3, v6, v7, v9], [v0, v4, v6, v7, v9], [v0, v1, v4, v6, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v1, v2, v4, v6, v7, v9], [v0, v3, v4, v6, v7, v9], [v0, v1, v3, v4, v6, v7, v9], [v0, v2, v3, v4, v6, v7, v9], [v0, v1, v2, v3, v4, v6, v7, v9], [v0, v5, v6, v7, v9], [v0, v1, v5, v6, v7, v9], [v0, v2, v5, v6, v7, v9], [v0, v1, v2, v5, v6, v7, v9], [v0, v3, v5, v6, v7, v9], [v0, v1, v3, v5, v6, v7, v9], [v0, v2, v3, v5, v6, v7, v9], [v0, v1, v2, v3, v5, v6, v7, v9], [v0, v4, v5, v6, v7, v9], [v0, v1, v4, v5, v6, v7, v9], [v0, v2, v4, v5, v6, v7, v9], [v0, v1, v2, v4, v5, v6, v7, v9], [v0, v3, v4, v5, v6, v7, v9], [v0, v1, v3, v4, v5, v6, v7, v9], [v0, v2, v3, v4, v5, v6, v7, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v9], [v0, v8, v9], [v0, v1, v8, v9], [v0, v2, v8, v9], [v0, v1, v2, v8, v9], [v0, v3, v8, v9], [v0, v1, v3, v8, v9], [v0, v2, v3, v8, v9], [v0, v1, v2, v3, v8, v9], [v0, v4, v8, v9], [v0, v1, v4, v8, v9], [v0, v2, v4, v8, v9], [v0, v1, v2, v4, v8, v9], [v0, v3, v4, v8, v9], [v0, v1, v3, v4, v8, v9], [v0, v2, v3, v4, v8, v9], [v0, v1, v2, v3, v4, v8, v9], [v0, v5, v8, v9], [v0, v1, v5, v8, v9], [v0, v2, v5, v8, v9], [v0, v1, v2, v5, v8, v9], [v0, v3, v5, v8, v9], [v0, v1, v3, v5, v8, v9], [v0, v2, v3, v5, v8, v9], [v0, v1, v2, v3, v5, v8, v9], [v0, v4, v5, v8, v9], [v0, v1, v4, v5, v8, v9], [v0, v2, v4, v5, v8, v9], [v0, v1, v2, v4, v5, v8, v9], [v0, v3, v4, v5, v8, v9], [v0, v1, v3, v4, v5, v8, v9], [v0, v2, v3, v4, v5, v8, v9], [v0, v1, v2, v3, v4, v5, v8, v9], [v0, v6, v8, v9], [v0, v1, v6, v8, v9], [v0, v2, v6, v8, v9], [v0, v1, v2, v6, v8, v9], [v0, v3, v6, v8, v9], [v0, v1, v3, v6, v8, v9], [v0, v2, v3, v6, v8, v9], [v0, v1, v2, v3, v6, v8, v9], [v0, v4, v6, v8, v9], [v0, v1, v4, v6, v8, v9], [v0, v2, v4, v6, v8, v9], [v0, v1, v2, v4, v6, v8, v9], [v0, v3, v4, v6, v8, v9], [v0, v1, v3, v4, v6, v8, v9], [v0, v2, v3, v4, v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v5, v6, v8, v9], [v0, v1, v5, v6, v8, v9], [v0, v2, v5, v6, v8, v9], [v0, v1, v2, v5, v6, v8, v9], [v0, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v4, v5, v6, v8, v9], [v0, v1, v4, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v7, v8, v9], [v0, v1, v7, v8, v9], [v0, v2, v7, v8, v9], [v0, v1, v2, v7, v8, v9], [v0, v3, v7, v8, v9], [v0, v1, v3, v7, v8, v9], [v0, v2, v3, v7, v8, v9], [v0, v1, v2, v3, v7, v8, v9], [v0, v4, v7, v8, v9], [v0, v1, v4, v7, v8, v9], [v0, v2, v4, v7, v8, v9], [v0, v1, v2, v4, v7, v8, v9], [v0, v3, v4, v7, v8, v9], [v0, v1, v3, v4, v7, v8, v9], [v0, v2, v3, v4, v7, v8, v9], [v0, v1, v2, v3, v4, v7, v8, v9], [v0, v5, v7, v8, v9], [v0, v1, v5, v7, v8, v9], [v0, v2, v5, v7, v8, v9], [v0, v1, v2, v5, v7, v8, v9], [v0, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v4, v5, v7, v8, v9], [v0, v1, v4, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v6, v7, v8, v9], [v0, v1, v6, v7, v8, v9], [v0, v2, v6, v7, v8, v9], [v0, v1, v2, v6, v7, v8, v9], [v0, v3, v6, v7, v8, v9], [v0, v1, v3, v6, v7, v8, v9], [v0, v2, v3, v6, v7, v8, v9], [v0, v1, v2, v3, v6, v7, v8, v9], [v0, v4, v6, v7, v8, v9], [v0, v1, v4, v6, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v5, v6, v7, v8, v9], [v0, v1, v5, v6, v7, v8, v9], [v0, v2, v5, v6, v7, v8, v9], [v0, v1, v2, v5, v6, v7, v8, v9], [v0, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v4, v5, v6, v7, v8, v9], [v0, v1, v4, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7], [v0, v8], [v0, v9]], [[v0], [v0, v1], [v0, v2], [v0, v1, v2], [v0, v3], [v0, v1, v3], [v0, v2, v3], [v0, v1, v2, v3], [v0, v4], [v0, v1, v4], [v0, v2, v4], [v0, v1, v2, v4], [v0, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v0, v1, v2, v3, v4], [v0, v5], [v0, v1, v5], [v0, v2, v5], [v0, v1, v2, v5], [v0, v3, v5], [v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v1, v2, v3, v5], [v0, v4, v5], [v0, v1, v4, v5], [v0, v2, v4, v5], [v0, v1, v2, v4, v5], [v0, v3, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v0, v1, v2, v3, v4, v5], [v0, v6], [v0, v1, v6], [v0, v2, v6], [v0, v1, v2, v6], [v0, v3, v6], [v0, v1, v3, v6], [v0, v2, v3, v6], [v0, v1, v2, v3, v6], [v0, v4, v6], [v0, v1, v4, v6], [v0, v2, v4, v6], [v0, v1, v2, v4, v6], [v0, v3, v4, v6], [v0, v1, v3, v4, v6], [v0, v2, v3, v4, v6], [v0, v1, v2, v3, v4, v6], [v0, v5, v6], [v0, v1, v5, v6], [v0, v2, v5, v6], 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v6, v8, v9], [v0, v1, v2, v3, v4, v6, v8, v9], [v0, v5, v6, v8, v9], [v0, v1, v5, v6, v8, v9], [v0, v2, v5, v6, v8, v9], [v0, v1, v2, v5, v6, v8, v9], [v0, v3, v5, v6, v8, v9], [v0, v1, v3, v5, v6, v8, v9], [v0, v2, v3, v5, v6, v8, v9], [v0, v1, v2, v3, v5, v6, v8, v9], [v0, v4, v5, v6, v8, v9], [v0, v1, v4, v5, v6, v8, v9], [v0, v2, v4, v5, v6, v8, v9], [v0, v1, v2, v4, v5, v6, v8, v9], [v0, v3, v4, v5, v6, v8, v9], [v0, v1, v3, v4, v5, v6, v8, v9], [v0, v2, v3, v4, v5, v6, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v8, v9], [v0, v7, v8, v9], [v0, v1, v7, v8, v9], [v0, v2, v7, v8, v9], [v0, v1, v2, v7, v8, v9], [v0, v3, v7, v8, v9], [v0, v1, v3, v7, v8, v9], [v0, v2, v3, v7, v8, v9], [v0, v1, v2, v3, v7, v8, v9], [v0, v4, v7, v8, v9], [v0, v1, v4, v7, v8, v9], [v0, v2, v4, v7, v8, v9], [v0, v1, v2, v4, v7, v8, v9], [v0, v3, v4, v7, v8, v9], [v0, v1, v3, v4, v7, v8, v9], [v0, v2, v3, v4, v7, v8, v9], [v0, v1, v2, v3, v4, v7, v8, v9], [v0, v5, v7, v8, v9], [v0, v1, v5, v7, v8, v9], [v0, v2, v5, v7, v8, v9], [v0, v1, v2, v5, v7, v8, v9], [v0, v3, v5, v7, v8, v9], [v0, v1, v3, v5, v7, v8, v9], [v0, v2, v3, v5, v7, v8, v9], [v0, v1, v2, v3, v5, v7, v8, v9], [v0, v4, v5, v7, v8, v9], [v0, v1, v4, v5, v7, v8, v9], [v0, v2, v4, v5, v7, v8, v9], [v0, v1, v2, v4, v5, v7, v8, v9], [v0, v3, v4, v5, v7, v8, v9], [v0, v1, v3, v4, v5, v7, v8, v9], [v0, v2, v3, v4, v5, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v7, v8, v9], [v0, v6, v7, v8, v9], [v0, v1, v6, v7, v8, v9], [v0, v2, v6, v7, v8, v9], [v0, v1, v2, v6, v7, v8, v9], [v0, v3, v6, v7, v8, v9], [v0, v1, v3, v6, v7, v8, v9], [v0, v2, v3, v6, v7, v8, v9], [v0, v1, v2, v3, v6, v7, v8, v9], [v0, v4, v6, v7, v8, v9], [v0, v1, v4, v6, v7, v8, v9], [v0, v2, v4, v6, v7, v8, v9], [v0, v1, v2, v4, v6, v7, v8, v9], [v0, v3, v4, v6, v7, v8, v9], [v0, v1, v3, v4, v6, v7, v8, v9], [v0, v2, v3, v4, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v6, v7, v8, v9], [v0, v5, v6, v7, v8, v9], [v0, v1, v5, v6, v7, v8, v9], [v0, v2, v5, v6, v7, v8, v9], [v0, v1, v2, v5, v6, v7, v8, v9], [v0, v3, v5, v6, v7, v8, v9], [v0, v1, v3, v5, v6, v7, v8, v9], [v0, v2, v3, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v5, v6, v7, v8, v9], [v0, v4, v5, v6, v7, v8, v9], [v0, v1, v4, v5, v6, v7, v8, v9], [v0, v2, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v4, v5, v6, v7, v8, v9], [v0, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v3, v4, v5, v6, v7, v8, v9], [v0, v2, v3, v4, v5, v6, v7, v8, v9], [v1, v2, v3, v4, v5, v6, v7, v8, v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9]], 1, [[v0]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0025/)

最小頂點覆蓋 · qf-mod46-mincover-exhaustive-minimizers · candidate





## 26. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"]],"candidate":["v0","v1","v2","v3"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], 是, 4, 2, [v0, v2], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3], 是, 4, 2, [v0, v2], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0026/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 27. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]],"candidate":["v0","v1","v2","v3","v4"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], 是, 5, 2, [v1, v3], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4], 是, 5, 2, [v1, v3], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0027/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 28. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"]],"candidate":["v0","v1","v2","v3","v4","v5"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], 是, 6, 3, [v0, v2, v4], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], 是, 6, 3, [v0, v2, v4], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0028/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 29. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"]],"candidate":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], 是, 7, 3, [v1, v3, v5], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], 是, 7, 3, [v1, v3, v5], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0029/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 30. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 4, [v0, v2, v4, v6], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 4, [v0, v2, v4, v6], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0030/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 31. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 4, [v1, v3, v5, v7], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 4, [v1, v3, v5, v7], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0031/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 32. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 5, [v0, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 5, [v0, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0032/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 33. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, 11, 5, [v1, v3, v5, v7, v9], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, 11, 5, [v1, v3, v5, v7, v9], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0033/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 34. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, 12, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, 12, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0034/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 35. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]],"candidate":["v0","v1","v2","v3"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], 是, 4, 2, [v0, v2], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3], 是, 4, 2, [v0, v2], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0035/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 36. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]],"candidate":["v0","v1","v2","v3","v4"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], 是, 5, 3, [v0, v1, v3], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4], 是, 5, 3, [v0, v1, v3], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0036/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 37. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v0"]],"candidate":["v0","v1","v2","v3","v4","v5"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], 是, 6, 3, [v0, v2, v4], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], 是, 6, 3, [v0, v2, v4], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0037/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 38. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], 是, 7, 4, [v0, v1, v3, v5], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], 是, 7, 4, [v0, v1, v3, v5], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0038/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 39. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 4, [v0, v2, v4, v6], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 4, [v0, v2, v4, v6], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0039/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 40. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 5, [v0, v1, v3, v5, v7], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 5, [v0, v1, v3, v5, v7], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0040/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 41. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 5, [v0, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 5, [v0, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0041/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 42. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, 11, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, 11, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0042/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 43. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"],["v11","v0"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, 12, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, 12, 6, [v0, v10, v2, v4, v6, v8], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0043/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 44. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"]],"candidate":["v0","v1","v2","v3"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], 是, 4, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3], 是, 4, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0044/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 45. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"]],"candidate":["v0","v1","v2","v3","v4"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4], 是, 5, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4], 是, 5, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0045/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 46. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"]],"candidate":["v0","v1","v2","v3","v4","v5"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5], 是, 6, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5], 是, 6, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0046/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 47. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"]],"candidate":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6], 是, 7, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6], 是, 7, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0047/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 48. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7], 是, 8, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0048/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 49. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"],["v0","v8"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, 9, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0049/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 50. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-nonminimum-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"],["v0","v8"],["v0","v9"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"]}。請依 [candidate, cover, candidate_size, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)

Wave6第九層核對=([v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, 10, 1, [v0], 否, explicit_smaller_cover_refutes_minimum_status)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0050/)

最小頂點覆蓋 · qf-mod46-mincover-nonminimum-witness · candidate





## 51. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1"],"edges":[["c0","l0_0"],["c0","l0_1"]],"candidate":["l0_0","l0_1"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1], [[l0_0, [l0_1], 否], [l0_1, [l0_0], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1], [[l0_0, [l0_1], 否], [l0_1, [l0_0], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0051/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 52. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"]],"candidate":["l0_0","l0_1","l0_2"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2], [[l0_0, [l0_1, l0_2], 否], [l0_1, [l0_0, l0_2], 否], [l0_2, [l0_0, l0_1], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2], [[l0_0, [l0_1, l0_2], 否], [l0_1, [l0_0, l0_2], 否], [l0_2, [l0_0, l0_1], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0052/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 53. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"]],"candidate":["l0_0","l0_1","l0_2","l0_3"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3], [[l0_0, [l0_1, l0_2, l0_3], 否], [l0_1, [l0_0, l0_2, l0_3], 否], [l0_2, [l0_0, l0_1, l0_3], 否], [l0_3, [l0_0, l0_1, l0_2], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3], [[l0_0, [l0_1, l0_2, l0_3], 否], [l0_1, [l0_0, l0_2, l0_3], 否], [l0_2, [l0_0, l0_1, l0_3], 否], [l0_3, [l0_0, l0_1, l0_2], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0053/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 54. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4], [[l0_0, [l0_1, l0_2, l0_3, l0_4], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4], [[l0_0, [l0_1, l0_2, l0_3, l0_4], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0054/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 55. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0055/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 56. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"],["c0","l0_6"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0056/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 57. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"],["c0","l0_6"],["c0","l0_7"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0057/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 58. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"],["c0","l0_6"],["c0","l0_7"],["c0","l0_8"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8], 否], [l0_8, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8], 否], [l0_8, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0058/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 59. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8","l0_9"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"],["c0","l0_6"],["c0","l0_7"],["c0","l0_8"],["c0","l0_9"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8","l0_9"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8, l0_9], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8, l0_9], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8, l0_9], 否], [l0_8, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_9], 否], [l0_9, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], [[l0_0, [l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_1, [l0_0, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_2, [l0_0, l0_1, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_3, [l0_0, l0_1, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_4, [l0_0, l0_1, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_5, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8, l0_9], 否], [l0_6, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8, l0_9], 否], [l0_7, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8, l0_9], 否], [l0_8, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_9], 否], [l0_9, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0059/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 60. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8","l0_9","l0_10"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c0","l0_4"],["c0","l0_5"],["c0","l0_6"],["c0","l0_7"],["c0","l0_8"],["c0","l0_9"],["c0","l0_10"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l0_4","l0_5","l0_6","l0_7","l0_8","l0_9","l0_10"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], [[l0_0, [l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_1, [l0_0, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_10, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_2, [l0_0, l0_1, l0_10, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_3, [l0_0, l0_1, l0_10, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_4, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_5, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8, l0_9], 否], [l0_6, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8, l0_9], 否], [l0_7, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8, l0_9], 否], [l0_8, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_9], 否], [l0_9, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], [[l0_0, [l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_1, [l0_0, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_10, [l0_0, l0_1, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_2, [l0_0, l0_1, l0_10, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_3, [l0_0, l0_1, l0_10, l0_2, l0_4, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_4, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_5, l0_6, l0_7, l0_8, l0_9], 否], [l0_5, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_6, l0_7, l0_8, l0_9], 否], [l0_6, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_7, l0_8, l0_9], 否], [l0_7, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_8, l0_9], 否], [l0_8, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_9], 否], [l0_9, [l0_0, l0_1, l0_10, l0_2, l0_3, l0_4, l0_5, l0_6, l0_7, l0_8], 否]], 是, 1, [c0], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0060/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 61. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"]],"candidate":["l0_0","l0_1","l1_0","l1_1"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1], [[l0_0, [l0_1, l1_0, l1_1], 否], [l0_1, [l0_0, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l1_1], 否], [l1_1, [l0_0, l0_1, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1], [[l0_0, [l0_1, l1_0, l1_1], 否], [l0_1, [l0_0, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l1_1], 否], [l1_1, [l0_0, l0_1, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0061/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 62. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0062/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 63. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0063/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 64. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0064/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 65. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0065/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 66. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"],["c1","l1_6"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], 否], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], 否], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0066/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 67. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6","l1_7"],"edges":[["c0","l0_0"],["c0","l0_1"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"],["c1","l1_6"],["c1","l1_7"]],"candidate":["l0_0","l0_1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6","l1_7"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], 否], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], 否], [l1_7, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], [[l0_0, [l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l0_1, [l0_0, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_0, [l0_0, l0_1, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_1, [l0_0, l0_1, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_2, [l0_0, l0_1, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6, l1_7], 否], [l1_3, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6, l1_7], 否], [l1_4, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6, l1_7], 否], [l1_5, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6, l1_7], 否], [l1_6, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_7], 否], [l1_7, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0067/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 68. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1], [[l0_0, [l0_1, l0_2, l1_0, l1_1], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1], [[l0_0, [l0_1, l0_2, l1_0, l1_1], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0068/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 69. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1","l1_2"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1","l1_2"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0069/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 70. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1","l1_2","l1_3"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1","l1_2","l1_3"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0070/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 71. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1","l1_2","l1_3","l1_4"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1","l1_2","l1_3","l1_4"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0071/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 72. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4, l1_5], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4, l1_5], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4, l1_5], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4, l1_5], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_5], 否], [l1_5, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0072/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 73. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","c1","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"],["c1","l1_3"],["c1","l1_4"],["c1","l1_5"],["c1","l1_6"]],"candidate":["l0_0","l0_1","l0_2","l1_0","l1_1","l1_2","l1_3","l1_4","l1_5","l1_6"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], 否], [l1_5, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], 否], [l1_6, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], [[l0_0, [l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_1, [l0_0, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l0_2, [l0_0, l0_1, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_0, [l0_0, l0_1, l0_2, l1_1, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_1, [l0_0, l0_1, l0_2, l1_0, l1_2, l1_3, l1_4, l1_5, l1_6], 否], [l1_2, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_3, l1_4, l1_5, l1_6], 否], [l1_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_4, l1_5, l1_6], 否], [l1_4, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_5, l1_6], 否], [l1_5, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_6], 否], [l1_6, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2, l1_3, l1_4, l1_5], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0073/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 74. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","c1","l1_0","l1_1"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c1","l1_0"],["c1","l1_1"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l1_0","l1_1"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l1_0, l1_1], [[l0_0, [l0_1, l0_2, l0_3, l1_0, l1_1], 否], [l0_1, [l0_0, l0_2, l0_3, l1_0, l1_1], 否], [l0_2, [l0_0, l0_1, l0_3, l1_0, l1_1], 否], [l0_3, [l0_0, l0_1, l0_2, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l0_2, l0_3, l1_1], 否], [l1_1, [l0_0, l0_1, l0_2, l0_3, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l1_0, l1_1], [[l0_0, [l0_1, l0_2, l0_3, l1_0, l1_1], 否], [l0_1, [l0_0, l0_2, l0_3, l1_0, l1_1], 否], [l0_2, [l0_0, l0_1, l0_3, l1_0, l1_1], 否], [l0_3, [l0_0, l0_1, l0_2, l1_0, l1_1], 否], [l1_0, [l0_0, l0_1, l0_2, l0_3, l1_1], 否], [l1_1, [l0_0, l0_1, l0_2, l0_3, l1_0], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0074/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 75. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-minimal-not-minimum；資料={"vertices":["c0","l0_0","l0_1","l0_2","l0_3","c1","l1_0","l1_1","l1_2"],"edges":[["c0","l0_0"],["c0","l0_1"],["c0","l0_2"],["c0","l0_3"],["c1","l1_0"],["c1","l1_1"],["c1","l1_2"]],"candidate":["l0_0","l0_1","l0_2","l0_3","l1_0","l1_1","l1_2"]}。請依 [candidate, deletion_rows, inclusion_minimal, minimum_size, smaller_cover, minimum, certificate] 欄序回答。

查看答案與解釋([l0_0, l0_1, l0_2, l0_3, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l0_2, l0_3, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l0_2, l0_3, l1_0, l1_1, l1_2], 否], [l0_2, [l0_0, l0_1, l0_3, l1_0, l1_1, l1_2], 否], [l0_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l0_2, l0_3, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l0_2, l0_3, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l0_2, l0_3, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)

Wave6第九層核對=([l0_0, l0_1, l0_2, l0_3, l1_0, l1_1, l1_2], [[l0_0, [l0_1, l0_2, l0_3, l1_0, l1_1, l1_2], 否], [l0_1, [l0_0, l0_2, l0_3, l1_0, l1_1, l1_2], 否], [l0_2, [l0_0, l0_1, l0_3, l1_0, l1_1, l1_2], 否], [l0_3, [l0_0, l0_1, l0_2, l1_0, l1_1, l1_2], 否], [l1_0, [l0_0, l0_1, l0_2, l0_3, l1_1, l1_2], 否], [l1_1, [l0_0, l0_1, l0_2, l0_3, l1_0, l1_2], 否], [l1_2, [l0_0, l0_1, l0_2, l0_3, l1_0, l1_1], 否]], 是, 2, [c0, c1], 否, inclusion_minimal_is_not_minimum)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0075/)

最小頂點覆蓋 · qf-mod46-mincover-minimal-not-minimum · candidate





## 76. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0076/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 77. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0077/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 78. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0078/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 79. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0079/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 80. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0080/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 81. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0081/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 82. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0082/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 83. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0083/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 84. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0084/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 85. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0085/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 86. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0086/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 87. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"empty_graph","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(empty_graph, [], 0, [[]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0087/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 88. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2"],"edges":[["v0","v1"],["v1","v2"],["v2","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v2], [v1, v2]], 2, [[v0, v1], [v0, v2], [v1, v2]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v2], [v1, v2]], 2, [[v0, v1], [v0, v2], [v1, v2]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0088/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 89. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v3], [v1, v2], [v2, v3]], 2, [[v0, v2], [v1, v3]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v3], [v1, v2], [v2, v3]], 2, [[v0, v2], [v1, v3]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0089/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 90. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v4], [v1, v2], [v2, v3], [v3, v4]], 3, [[v0, v1, v3], [v0, v2, v3], [v0, v2, v4], [v1, v2, v4], [v1, v3, v4]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v4], [v1, v2], [v2, v3], [v3, v4]], 3, [[v0, v1, v3], [v0, v2, v3], [v0, v2, v4], [v1, v2, v4], [v1, v3, v4]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0090/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 91. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v5], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], 3, [[v0, v2, v4], [v1, v3, v5]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v5], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], 3, [[v0, v2, v4], [v1, v3, v5]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0091/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 92. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v6], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], 4, [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v2, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v6], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], 4, [[v0, v1, v3, v5], [v0, v2, v3, v5], [v0, v2, v4, v5], [v0, v2, v4, v6], [v1, v2, v4, v6], [v1, v3, v4, v6], [v1, v3, v5, v6]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0092/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 93. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v7], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], 4, [[v0, v2, v4, v6], [v1, v3, v5, v7]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v7], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], 4, [[v0, v2, v4, v6], [v1, v3, v5, v7]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0093/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 94. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], 5, [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v8], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8]], 5, [[v0, v1, v3, v5, v7], [v0, v2, v3, v5, v7], [v0, v2, v4, v5, v7], [v0, v2, v4, v6, v7], [v0, v2, v4, v6, v8], [v1, v2, v4, v6, v8], [v1, v3, v4, v6, v8], [v1, v3, v5, v6, v8], [v1, v3, v5, v7, v8]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0094/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 95. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v9], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v3, v5, v7, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v9], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 5, [[v0, v2, v4, v6, v8], [v1, v3, v5, v7, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0095/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 96. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v10], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v2, v4, v6, v8, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v10], [v1, v2], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v10, v2, v4, v6, v8], [v1, v10, v3, v4, v6, v8], [v1, v10, v3, v5, v6, v8], [v1, v10, v3, v5, v7, v8], [v0, v1, v3, v5, v7, v9], [v1, v10, v3, v5, v7, v9], [v0, v2, v3, v5, v7, v9], [v0, v2, v4, v5, v7, v9], [v0, v2, v4, v6, v7, v9], [v0, v2, v4, v6, v8, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0096/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 97. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"],["v6","v7"],["v7","v8"],["v8","v9"],["v9","v10"],["v10","v11"],["v11","v0"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v11], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v11, v3, v5, v7, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v11], [v1, v2], [v10, v11], [v10, v9], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7], [v7, v8], [v8, v9]], 6, [[v0, v10, v2, v4, v6, v8], [v1, v11, v3, v5, v7, v9]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0097/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 98. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v1","v2"],["v1","v3"],["v2","v3"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v1, v2], [v1, v3], [v2, v3]], 3, [[v0, v1, v2], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v1, v2], [v1, v3], [v2, v3]], 3, [[v0, v1, v2], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0098/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 99. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v1","v2"],["v1","v3"],["v1","v4"],["v2","v3"],["v2","v4"],["v3","v4"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v1, v2], [v1, v3], [v1, v4], [v2, v3], [v2, v4], [v3, v4]], 4, [[v0, v1, v2, v3], [v0, v1, v2, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v1, v2], [v1, v3], [v1, v4], [v2, v3], [v2, v4], [v3, v4]], 4, [[v0, v1, v2, v3], [v0, v1, v2, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0099/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate





## 100. 最小頂點覆蓋

bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-empty-multiple-boundary；資料={"mode":"multiple_minima","vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v1","v2"],["v1","v3"],["v1","v4"],["v1","v5"],["v2","v3"],["v2","v4"],["v2","v5"],["v3","v4"],["v3","v5"],["v4","v5"]]}。請依 [mode, edges, minimum_size, minimum_covers, mode_certificate, boundary] 欄序回答。

empty_graph是無邊圖，vertex carrier仍非空；唯一minimum cover為空集。multiple_minima列出全部最小解，不宣稱唯一。

查看答案與解釋(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v1, v2], [v1, v3], [v1, v4], [v1, v5], [v2, v3], [v2, v4], [v2, v5], [v3, v4], [v3, v5], [v4, v5]], 5, [[v0, v1, v2, v3, v4], [v0, v1, v2, v3, v5], [v0, v1, v2, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)

Wave6第九層核對=(multiple_minima, [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v1, v2], [v1, v3], [v1, v4], [v1, v5], [v2, v3], [v2, v4], [v2, v5], [v3, v4], [v3, v5], [v4, v5]], 5, [[v0, v1, v2, v3, v4], [v0, v1, v2, v3, v5], [v0, v1, v2, v4, v5], [v0, v1, v3, v4, v5], [v0, v2, v3, v4, v5], [v1, v2, v3, v4, v5]], 是, empty_graph_has_unique_empty_minimum_cover_while_other_graphs_may_have_multiple_minima_without_Konig_or_weighted_claims)；依完整明示資料獨立重算；minimum cardinality與全部minimizers由完整枚舉取得；nonminimum需更小cover witness；inclusion-minimal不是minimum；保留empty/multiple minima且不混同edge cover、independent set、König或weighted/directed variants。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r06-minimum-vertex-cover-0100/)

最小頂點覆蓋 · qf-mod46-mincover-empty-multiple-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r06-minimum-vertex-cover-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r06-minimum-vertex-cover-foundations/validation-report.json)