Eulerian orientations and vertex-connectivity

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