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
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
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）
頂點覆蓋 · qf-mod45-vcover-minimal-vs-minimum-boundary · candidate
原始題目 JSONL · 驗收報告