# Euler trail與circuit基礎 · 脈衝 R04

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-20261014-advance-20261105-r04-eulerian-trail-foundations · 2026-10-14 · 100 題

欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。

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



## 1. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":3,"edges":[[0,1],[0,2],[1,2]],"vertex_walk":[0,1,2,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 0], [0, 2, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 0], [0, 2, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0001/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 2. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":4,"edges":[[0,1],[0,3],[1,2],[2,3]],"vertex_walk":[0,1,2,3,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 0], [0, 2, 3, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 0], [0, 2, 3, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0002/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 3. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":5,"edges":[[0,1],[0,4],[1,2],[2,3],[3,4]],"vertex_walk":[0,1,2,3,4,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 0], [0, 2, 3, 4, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 0], [0, 2, 3, 4, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0003/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 4. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":6,"edges":[[0,1],[0,5],[1,2],[2,3],[3,4],[4,5]],"vertex_walk":[0,1,2,3,4,5,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 0], [0, 2, 3, 4, 5, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 0], [0, 2, 3, 4, 5, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0004/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 5. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":7,"edges":[[0,1],[0,6],[1,2],[2,3],[3,4],[4,5],[5,6]],"vertex_walk":[0,1,2,3,4,5,6,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 0], [0, 2, 3, 4, 5, 6, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 0], [0, 2, 3, 4, 5, 6, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0005/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 6. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":8,"edges":[[0,1],[0,7],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]],"vertex_walk":[0,1,2,3,4,5,6,7,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 0], [0, 2, 3, 4, 5, 6, 7, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 0], [0, 2, 3, 4, 5, 6, 7, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0006/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 7. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":9,"edges":[[0,1],[0,8],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8]],"vertex_walk":[0,1,2,3,4,5,6,7,8,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 0], [0, 2, 3, 4, 5, 6, 7, 8, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 0], [0, 2, 3, 4, 5, 6, 7, 8, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0007/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 8. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":10,"edges":[[0,1],[0,9],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0008/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 9. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":11,"edges":[[0,1],[0,10],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0009/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 10. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":12,"edges":[[0,1],[0,11],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0010/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 11. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":13,"edges":[[0,1],[0,12],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0011/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 12. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":14,"edges":[[0,1],[0,13],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0012/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 13. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":15,"edges":[[0,1],[0,14],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0013/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 14. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":16,"edges":[[0,1],[0,15],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0014/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 15. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":17,"edges":[[0,1],[0,16],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0015/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 16. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":18,"edges":[[0,1],[0,17],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0016/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 17. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":19,"edges":[[0,1],[0,18],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0017/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 18. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":20,"edges":[[0,1],[0,19],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0018/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 19. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":21,"edges":[[0,1],[0,20],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0019/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 20. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":22,"edges":[[0,1],[0,21],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0020/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 21. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":23,"edges":[[0,1],[0,22],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0021/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 22. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":24,"edges":[[0,1],[0,23],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0022/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 23. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":25,"edges":[[0,1],[0,24],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0023/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 24. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":26,"edges":[[0,1],[0,25],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0024/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 25. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":27,"edges":[[0,1],[0,26],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26]],"vertex_walk":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,0]}。請依 [vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 0], [0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0025/)

Euler trail與circuit · qf-mod36-euler-trail-audit · candidate





## 26. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":2,"edges":[[0,1]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 1], [0, 1], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 1], [0, 1], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0026/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 27. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":3,"edges":[[0,1],[1,2]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 1], [0, 2], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 1], [0, 2], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0027/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 28. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":4,"edges":[[0,1],[1,2],[2,3]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 1], [0, 3], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 1], [0, 3], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0028/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 29. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":5,"edges":[[0,1],[1,2],[2,3],[3,4]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 1], [0, 4], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 1], [0, 4], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0029/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 30. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":6,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 1], [0, 5], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 1], [0, 5], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0030/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 31. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":7,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 1], [0, 6], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 1], [0, 6], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0031/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 32. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":8,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 1], [0, 7], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 1], [0, 7], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0032/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 33. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":9,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 1], [0, 8], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 1], [0, 8], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0033/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 34. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":10,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 9], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 9], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0034/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 35. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":11,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 10], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 10], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0035/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 36. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":12,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 11], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 11], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0036/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 37. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":13,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 12], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 12], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0037/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 38. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":14,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 13], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 13], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0038/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 39. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":15,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 14], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 14], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0039/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 40. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":16,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 15], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 15], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0040/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 41. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":17,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 16], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 16], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0041/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 42. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":18,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 17], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 17], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0042/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 43. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":19,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 18], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 18], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0043/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 44. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":20,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 19], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 19], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0044/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 45. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":21,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 20], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 20], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0045/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 46. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":22,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 21], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 21], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0046/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 47. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":23,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 22], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 22], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0047/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 48. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":24,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 23], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 23], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0048/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 49. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":25,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 24], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 24], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0049/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 50. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-odd-degree-classification；資料={"n":26,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25]]}。請依 [degrees, odd_vertices, edge_support_connected, euler_type, criterion] 欄序回答。

查看答案與解釋([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 25], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)

Wave5第五層核對=([1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1], [0, 25], 是, open_euler_trail, zero_or_two_odd_vertices_on_connected_edge_support)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0050/)

Euler trail與circuit · qf-mod36-euler-odd-degree-classification · candidate





## 51. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":3,"edges":[[0,1]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1], 是, 否, [0, 1], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1], 是, 否, [0, 1], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0051/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 52. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":4,"edges":[[0,1],[1,2]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2], 是, 否, [0, 2], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2], 是, 否, [0, 2], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0052/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 53. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":5,"edges":[[0,1],[1,2],[2,3]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3], 是, 否, [0, 3], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3], 是, 否, [0, 3], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0053/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 54. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":6,"edges":[[0,1],[1,2],[2,3],[3,4]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4], 是, 否, [0, 4], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4], 是, 否, [0, 4], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0054/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 55. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":7,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5], 是, 否, [0, 5], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5], 是, 否, [0, 5], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0055/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 56. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":8,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6], 是, 否, [0, 6], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6], 是, 否, [0, 6], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0056/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 57. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":9,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7], 是, 否, [0, 7], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7], 是, 否, [0, 7], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0057/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 58. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":10,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 否, [0, 8], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8], 是, 否, [0, 8], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0058/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 59. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":11,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, 否, [0, 9], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 是, 否, [0, 9], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0059/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 60. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":12,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 是, 否, [0, 10], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 是, 否, [0, 10], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0060/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 61. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":13,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, 否, [0, 11], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], 是, 否, [0, 11], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0061/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 62. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":14,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 是, 否, [0, 12], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], 是, 否, [0, 12], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0062/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 63. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":15,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, 否, [0, 13], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], 是, 否, [0, 13], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0063/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 64. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":16,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], 是, 否, [0, 14], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], 是, 否, [0, 14], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0064/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 65. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":17,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 是, 否, [0, 15], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], 是, 否, [0, 15], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0065/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 66. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":18,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 是, 否, [0, 16], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 是, 否, [0, 16], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0066/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 67. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":19,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 是, 否, [0, 17], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], 是, 否, [0, 17], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0067/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 68. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":20,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 是, 否, [0, 18], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], 是, 否, [0, 18], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0068/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 69. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":21,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 是, 否, [0, 19], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], 是, 否, [0, 19], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0069/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 70. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":22,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 是, 否, [0, 20], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], 是, 否, [0, 20], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0070/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 71. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":23,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 是, 否, [0, 21], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], 是, 否, [0, 21], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0071/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 72. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":24,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], 是, 否, [0, 22], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], 是, 否, [0, 22], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0072/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 73. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":25,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 是, 否, [0, 23], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 是, 否, [0, 23], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0073/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 74. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":26,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 是, 否, [0, 24], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], 是, 否, [0, 24], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0074/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 75. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-support-connectivity；資料={"n":27,"edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25]]}。請依 [nonisolated_vertices, edge_support_connected, whole_graph_connected, odd_vertices, euler_type, boundary] 欄序回答。

查看答案與解釋([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], 是, 否, [0, 25], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)

Wave5第五層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], 是, 否, [0, 25], open_euler_trail, isolated_vertices_do_not_break_edge_support_connectivity)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0075/)

Euler trail與circuit · qf-mod36-euler-support-connectivity · candidate





## 76. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":1}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(1, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(1, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0076/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 77. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":2}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(2, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(2, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0077/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 78. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":3}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(3, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(3, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0078/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 79. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":4}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(4, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(4, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0079/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 80. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":5}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(5, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(5, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0080/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 81. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":6}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(6, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(6, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0081/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 82. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":7}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(7, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(7, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0082/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 83. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":8}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(8, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(8, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0083/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 84. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":9}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(9, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(9, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0084/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 85. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":10}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(10, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(10, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0085/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 86. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":11}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(11, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(11, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0086/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 87. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":12}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(12, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(12, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0087/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 88. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":13}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(13, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(13, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0088/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 89. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":14}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(14, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(14, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0089/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 90. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":15}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(15, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(15, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0090/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 91. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":16}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(16, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(16, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0091/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 92. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":17}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(17, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(17, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0092/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 93. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":18}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(18, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(18, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0093/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 94. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":19}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(19, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(19, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0094/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 95. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":20}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(20, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(20, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0095/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 96. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":21}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(21, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(21, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0096/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 97. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":22}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(22, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(22, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0097/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 98. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":23}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(23, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(23, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0098/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 99. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":24}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(24, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(24, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0099/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate





## 100. Euler trail與circuit

完整有限簡單無向圖、edge support與明示walk。操作=euler-zero-edge-convention；資料={"n":25}。請依 [vertex_count, edge_count, length_zero_circuit, convention, boundary] 欄序回答。

查看答案與解釋(25, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)

Wave5第五層核對=(25, 0, 是, length_zero_circuit_on_nonempty_vertex_set, empty_vertex_graph_out_of_scope)；依完整明示資料獨立重算；trail可重複頂點但不可重複邊；0或2個奇度判準還要求非孤立頂點同一分量；孤立點不破壞非零邊support；零邊非空圖採length-zero circuit且不推Hamilton性質。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r04-eulerian-trail-0100/)

Euler trail與circuit · qf-mod36-euler-zero-edge-convention · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r04-eulerian-trail-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r04-eulerian-trail-foundations/validation-report.json)