第 26027 題：最小頂點覆蓋

原題與已知條件

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

• G001 — bounded finite simple graph的全部vertex subsets與all-edge cover audit。操作=mincover-exhaustive-minimizers；資料={"vertices":["v0","v1","v2","v3","v4"],"edges":[["v0","v1"],["v1","v2"],["v2","v3"],["v3","v4"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-minimum-vertex-cover

逐步推導

source roles = [mincover-exhaustive-minimizers]

derived = [[vertices, edges, all_covers, minimum_size, minimum_covers, certificate]]

source roles = [[v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], null]

derived = [[v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], null]

source roles = [[v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], 32]

derived = [[10, 11, 13, 14, 15, 21, 22, 23, 26, 27, 29, 30, 31], [[0, 0], [1, 1], [2, 2], [3, 2], [4, 0], [5, 3], [6, 3], [7, 3], [8, 0], [9, 1], [12, 0], [16, 0], [17, 1], [18, 2], [19, 2], [20, 0], [24, 0], [25, 1], [28, 0]], [[v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], [0, 0, 1, 6, 5, 1], 2, [[v1, v3]]]

逐步反向核對

• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

([v0, v1, v2, v3, v4], [[v0, v1], [v1, v2], [v2, v3], [v3, v4]], [[v1, v3], [v0, v1, v3], [v0, v2, v3], [v1, v2, v3], [v0, v1, v2, v3], [v0, v2, v4], [v1, v2, v4], [v0, v1, v2, v4], [v1, v3, v4], [v0, v1, v3, v4], [v0, v2, v3, v4], [v1, v2, v3, v4], [v0, v1, v2, v3, v4]], 2, [[v1, v3]], all_vertex_subsets_are_audited_before_selecting_all_minimizers)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。