# 頂點覆蓋基礎 · 脈衝 R07

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-20261114-r07-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. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"]],"candidate":["v1","v2","v3"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], [[v0, v1], [v1, v2], [v2, v3]], [v1, v2, v3], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3], [[v0, v1], [v1, v2], [v2, v3]], [v1, v2, v3], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0001/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 2. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]],"candidate":["v0","v2","v3","v4"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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]], [v0, v2, v3, v4], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], [v0, v2, v3, v4], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0002/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 3. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"]],"candidate":["v0","v1","v3","v4","v5"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v3, v4, v5], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [v0, v1, v3, v4, v5], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0003/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 4. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v4","v5","v6"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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]], [v0, v1, v2, v4, v5, v6], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [v0, v1, v2, v4, v5, v6], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0004/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 5. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v5","v6","v7"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v5, v6, v7], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6], [v6, v7]], [v0, v1, v2, v3, v5, v6, v7], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0005/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 6. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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]], [v0, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0006/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 7. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v7","v8","v9"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4, v5, v7, v8, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v2, v3, v4, v5, v7, v8, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0007/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 8. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v8","v9","v10"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v10, v2, v3, v4, v5, v6, v8, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v10, v2, v3, v4, v5, v6, v8, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0008/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 9. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v9","v10","v11"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v10, v11], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v10, v11, v2, v3, v4, v5, v6, v7, v9], [[[v0, v1], 是], [[v1, v2], 是], [[v10, v11], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0009/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 10. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]],"candidate":["v0","v2","v3"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v3], [[[v0, v1], 是], [[v0, v3], 是], [[v1, v2], 是], [[v2, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3], [[v0, v1], [v0, v3], [v1, v2], [v2, v3]], [v0, v2, v3], [[[v0, v1], 是], [[v0, v3], 是], [[v1, v2], 是], [[v2, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0010/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 11. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]],"candidate":["v1","v2","v3","v4"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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]], [v1, v2, v3, v4], [[[v0, v1], 是], [[v0, v4], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v0, v4], [v1, v2], [v2, v3], [v3, v4]], [v1, v2, v3, v4], [[[v0, v1], 是], [[v0, v4], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0011/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 12. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4], [[[v0, v1], 是], [[v0, v5], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v5], [v1, v2], [v2, v3], [v3, v4], [v4, v5]], [v0, v1, v2, v3, v4], [[[v0, v1], 是], [[v0, v5], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0012/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 13. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v2, v3, v4, v6], [[[v0, v1], 是], [[v0, v6], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v6], [v1, v2], [v2, v3], [v3, v4], [v4, v5], [v5, v6]], [v0, v1, v2, v3, v4, v6], [[[v0, v1], 是], [[v0, v6], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0013/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 14. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4, v6, v7], [[[v0, v1], 是], [[v0, v7], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v2, v3, v4, v6, v7], [[[v0, v1], 是], [[v0, v7], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0014/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 15. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v8], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0015/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 16. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8","v9"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v9], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v9], 是], [[v1, v2], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0016/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 17. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8","v9","v10"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v10, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v10], 是], [[v1, v2], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v10, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v10], 是], [[v1, v2], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0017/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 18. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8","v9","v10","v11"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v11], 是], [[v1, v2], 是], [[v10, v11], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v10, v11, v2, v3, v4, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v11], 是], [[v1, v2], 是], [[v10, v11], 是], [[v10, v9], 是], [[v2, v3], 是], [[v3, v4], 是], [[v4, v5], 是], [[v5, v6], 是], [[v6, v7], 是], [[v7, v8], 是], [[v8, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0018/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 19. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"]],"candidate":["v0","v1","v3"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, certificate] 欄序回答。

查看答案與解釋([v0, v1, v2, v3], [[v0, v1], [v0, v2], [v0, v3]], [v0, v1, v3], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3], [[v0, v1], [v0, v2], [v0, v3]], [v0, v1, v3], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0019/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 20. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"]],"candidate":["v0","v1","v2","v3"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4], [[v0, v1], [v0, v2], [v0, v3], [v0, v4]], [v0, v1, v2, v3], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0020/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 21. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"]],"candidate":["v0","v1","v3","v4","v5"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v3, v4, v5], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5]], [v0, v1, v3, v4, v5], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0021/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 22. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"]],"candidate":["v1","v2","v3","v4","v5","v6"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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]], [v1, v2, v3, v4, v5, v6], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6]], [v1, v2, v3, v4, v5, v6], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0022/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 23. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v7"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4, v5, v7], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([v0, v1, v2, v3, v4, v5, v6, v7], [[v0, v1], [v0, v2], [v0, v3], [v0, v4], [v0, v5], [v0, v6], [v0, v7]], [v0, v1, v2, v3, v4, v5, v7], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0023/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 24. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v6","v7","v8"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是], [[v0, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v2, v3, v4, v6, v7, v8], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是], [[v0, v8], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0024/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 25. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-complete-edge-audit；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","v5","v6","v7","v8","v9"]}。請依 [vertices, edges, candidate, edge_coverage_rows, cover, uncovered_edge_or_null, 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, v1, v2, v3, v5, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是], [[v0, v8], 是], [[v0, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)

Wave6第八層核對=([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, v1, v2, v3, v5, v6, v7, v8, v9], [[[v0, v1], 是], [[v0, v2], 是], [[v0, v3], 是], [[v0, v4], 是], [[v0, v5], 是], [[v0, v6], 是], [[v0, v7], 是], [[v0, v8], 是], [[v0, v9], 是]], 是, null, vertex_cover_requires_every_edge_to_have_at_least_one_selected_endpoint)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0025/)

頂點覆蓋 · qf-mod45-vcover-complete-edge-audit · candidate





## 26. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

查看答案與解釋([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0026/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 27. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0027/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 28. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0028/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 29. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0029/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 30. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0030/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 31. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0031/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 32. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0032/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 33. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v10, v9], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0033/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 34. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v1, v2], 否], [[v10, v11], 否], [[v10, v9], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0034/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 35. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

查看答案與解釋([], [[[v0, v1], 否], [[v0, v3], 否], [[v1, v2], 否], [[v2, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v3], 否], [[v1, v2], 否], [[v2, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0035/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 36. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v4], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0036/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 37. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v0"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v5], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0037/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 38. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v6], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0038/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 39. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v7], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0039/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 40. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v8], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0040/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 41. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v9], 否], [[v1, v2], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0041/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 42. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v10], 否], [[v1, v2], 否], [[v10, v9], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0042/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 43. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v11], 否], [[v1, v2], 否], [[v10, v11], 否], [[v10, v9], 否], [[v2, v3], 否], [[v3, v4], 否], [[v4, v5], 否], [[v5, v6], 否], [[v6, v7], 否], [[v7, v8], 否], [[v8, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0043/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 44. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

查看答案與解釋([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0044/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 45. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0045/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 46. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-witness；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"]],"candidate":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否], [[v0, v5], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0046/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 47. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否], [[v0, v5], 否], [[v0, v6], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0047/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 48. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否], [[v0, v5], 否], [[v0, v6], 否], [[v0, v7], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0048/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 49. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否], [[v0, v5], 否], [[v0, v6], 否], [[v0, v7], 否], [[v0, v8], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0049/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 50. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-uncovered-edge-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":[]}。請依 [candidate, edge_coverage_rows, uncovered_edge, cover, boundary] 欄序回答。

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

Wave6第八層核對=([], [[[v0, v1], 否], [[v0, v2], 否], [[v0, v3], 否], [[v0, v4], 否], [[v0, v5], 否], [[v0, v6], 否], [[v0, v7], 否], [[v0, v8], 否], [[v0, v9], 否]], [v0, v1], 否, one_edge_with_both_endpoints_outside_C_refutes_vertex_cover)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0050/)

頂點覆蓋 · qf-mod45-vcover-uncovered-edge-witness · candidate





## 51. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1"],"edges":[],"candidate":[],"superset":["v1"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(是, 是, [v0, v1], [], 是, [v1], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(是, 是, [v0, v1], [], 是, [v1], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0051/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 52. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"]],"candidate":["v0","v1","v2"],"superset":["v0","v1","v2","v3"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0052/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 53. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"]],"candidate":["v0","v1","v2","v3"],"superset":["v0","v1","v2","v3","v4"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0053/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 54. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]],"candidate":["v0","v1","v2","v3","v4"],"superset":["v0","v1","v2","v3","v4","v5"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0054/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 55. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"]],"candidate":["v0","v1","v2","v3","v4","v5"],"superset":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v6], [v0, v1, v2, v3, v4, v5], 是, [v0, v1, v2, v3, v4, v5, v6], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0055/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 56. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v6"]],"candidate":["v0","v1","v2","v3","v4","v5","v6"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v7], [v0, v1, v2, v3, v4, v5, v6], 是, [v0, v1, v2, v3, v4, v5, v6, v7], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0056/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 57. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v8], [v0, v1, v2, v3, v4, v5, v6, v7], 是, [v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0057/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 58. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0058/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 59. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v10], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0059/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 60. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v11], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0060/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 61. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2"],"edges":[["v0","v1"]],"candidate":["v0","v1"],"superset":["v0","v1","v2"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v2], [v0, v1], 是, [v0, v1, v2], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v2], [v0, v1], 是, [v0, v1, v2], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0061/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 62. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v0","v2"]],"candidate":["v0","v1","v2"],"superset":["v0","v1","v2","v3"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0062/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 63. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"]],"candidate":["v0","v1","v2","v3"],"superset":["v0","v1","v2","v3","v4"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0063/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 64. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"]],"candidate":["v0","v1","v2","v3","v4"],"superset":["v0","v1","v2","v3","v4","v5"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0064/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 65. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"]],"candidate":["v0","v1","v2","v3","v4","v5"],"superset":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v6], [v0, v1, v2, v3, v4, v5], 是, [v0, v1, v2, v3, v4, v5, v6], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0065/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 66. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"]],"candidate":["v0","v1","v2","v3","v4","v5","v6"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v7], [v0, v1, v2, v3, v4, v5, v6], 是, [v0, v1, v2, v3, v4, v5, v6, v7], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0066/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 67. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v8], [v0, v1, v2, v3, v4, v5, v6, v7], 是, [v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0067/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 68. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；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"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v9], [v0, v1, v2, v3, v4, v5, v6, v7, v8], 是, [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0068/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 69. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"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"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v10], [v0, v1, v2, v3, v4, v5, v6, v7, v8, v9], 是, [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0069/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 70. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"],"edges":[["v0","v1"],["v0","v2"],["v0","v3"],["v0","v4"],["v0","v5"],["v0","v6"],["v0","v7"],["v0","v8"],["v0","v9"],["v0","v10"]],"candidate":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10"],"superset":["v0","v1","v2","v3","v4","v5","v6","v7","v8","v9","v10","v11"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v11], [v0, v1, v10, v2, v3, v4, v5, v6, v7, v8, v9], 是, [v0, v1, v10, v11, v2, v3, v4, v5, v6, v7, v8, v9], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0070/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 71. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2"],"edges":[],"candidate":["v0","v1"],"superset":["v0","v1","v2"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(是, 是, [v0, v1, v2], [v0, v1], 是, [v0, v1, v2], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(是, 是, [v0, v1, v2], [v0, v1], 是, [v0, v1, v2], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0071/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 72. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3"],"edges":[["v0","v1"],["v1","v2"],["v2","v0"]],"candidate":["v0","v1","v2"],"superset":["v0","v1","v2","v3"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v3], [v0, v1, v2], 是, [v0, v1, v2, v3], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0072/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 73. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v0"]],"candidate":["v0","v1","v2","v3"],"superset":["v0","v1","v2","v3","v4"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v4], [v0, v1, v2, v3], 是, [v0, v1, v2, v3, v4], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0073/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 74. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v0"]],"candidate":["v0","v1","v2","v3","v4"],"superset":["v0","v1","v2","v3","v4","v5"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

查看答案與解釋(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)

Wave6第八層核對=(否, null, [v5], [v0, v1, v2, v3, v4], 是, [v0, v1, v2, v3, v4, v5], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0074/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 75. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-empty-isolated-superset；資料={"vertices":["v0","v1","v2","v3","v4","v5","v6"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"],["v4","v5"],["v5","v0"]],"candidate":["v0","v1","v2","v3","v4","v5"],"superset":["v0","v1","v2","v3","v4","v5","v6"]}。請依 [edgeless_graph, empty_cover_valid_if_edgeless_or_null, isolated_vertices, candidate, candidate_cover, superset, superset_cover, certificate] 欄序回答。

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

Wave6第八層核對=(否, null, [v6], [v0, v1, v2, v3, v4, v5], 是, [v0, v1, v2, v3, v4, v5, v6], 是, empty_edge_graph_empty_cover_is_valid_isolated_vertices_are_optional_and_cover_supersets_remain_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0075/)

頂點覆蓋 · qf-mod45-vcover-empty-isolated-superset · candidate





## 76. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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

Wave6第八層核對=([l0_0, l0_1], [[l0_0, [l0_1], 否], [l0_1, [l0_0], 否]], 是, 1, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0076/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 77. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0077/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 78. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0078/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 79. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0079/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 80. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0080/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 81. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0081/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 82. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0082/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 83. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0083/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 84. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0084/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 85. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0085/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 86. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0086/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 87. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0087/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 88. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0088/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 89. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0089/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 90. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0090/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 91. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0091/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 92. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0092/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 93. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0093/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 94. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0094/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 95. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0095/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 96. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0096/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 97. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0097/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 98. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0098/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 99. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0099/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate





## 100. 頂點覆蓋

有限simple undirected graph的全部edges與candidate subset完整核對。操作=vcover-minimal-vs-minimum-boundary；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, minimum, minimality_tests_agree, certificate] 欄序回答。

minimality_tests_agree只比較此candidate的兩個旗標；兩者同為否時也可為是，不是宣稱minimal與minimum一般等價。

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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)

Wave6第八層核對=([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, 否, 否, inclusion_minimal_means_no_single_deletion_while_minimum_compares_all_covers)；依完整明示資料獨立重算；uncovered edge是反例；empty-edge、isolated vertex與cover superset邊界分開；inclusion-minimal不是minimum；不混用edge cover、independent set或directed cover。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r07-vertex-cover-0100/)

頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r07-vertex-cover-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r07-vertex-cover-foundations/validation-report.json)