Abstract Collapsible graphs are introduced by Caltin to study Eulerian subgraphs, and S-group-connectivity is introduced by Jaeger et al. to study flows of graphs. Lai established a connection of those graph classes by showing that collapsible graphs have S-connectivity for group S of order 4. In a survey paper in 2011, Lai et al. conjectured that this property holds for all finite Abelian groups of size at least 4. We prove this conjecture for all groups of even order |S| ≥ 4 and of large odd order |S| ≥ 53.

中文翻译：

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欧拉子图和图的 S-连通性

摘要 Caltin 引入了可折叠图来研究欧拉子图，Jaeger 等人引入了 S 群连通性。研究图流。Lai 通过证明可折叠图对 4 阶 S 组具有 S 连通性来建立这些图类的连接。在 2011 年的一篇调查论文中，Lai 等人。推测该性质适用于所有大小至少为 4 的有限阿贝尔群。我们证明该猜想适用于所有偶数阶 |S| 的群。≥ 4 且具有大奇数阶 |S| ≥ 53。