Abstract It is well-known that every Eulerian orientation of an Eulerian 2 k -edge-connected undirected graph is k -arc-connected. A long-standing goal in the area has been to obtain analogous results for vertex-connectivity. Levit, Chandran and Cheriyan recently proved in Levit et al. (2018) that every Eulerian orientation of a hypercube of dimension 2 k is k -vertex-connected. Here we provide an elementary proof for this result. We also show other families of 2 k -regular graphs for which every Eulerian orientation is k -vertex-connected, namely the even regular complete bipartite graphs, the incidence graphs of projective planes of odd order, the line graphs of regular complete bipartite graphs and the line graphs of complete graphs. Furthermore, we provide a simple graph counterexample for a conjecture of Frank attempting to characterize graphs admitting at least one k -vertex-connected orientation.

中文翻译：

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欧拉方向和顶点连通性

摘要 众所周知，欧拉 2 k 边连通无向图的每个欧拉方向都是 k 弧连通的。该领域的一个长期目标是获得顶点连通性的类似结果。Levit、Chandran 和 Cheriyan 最近在 Levit 等人中得到了证明。(2018) 2 k 维超立方体的每个欧拉方向都是 k 顶点连接的。这里我们为这个结果提供了一个基本的证明。我们还展示了其他 2 k 正则图族，其中每个欧拉方向都是 k 顶点连通的，即偶正则完全二部图、奇数阶射影平面的关联图、规则完全二部图的线图和完全图的折线图。此外，