On Eulerian orientations of even-degree hypercubes

Maxwell Levit; L. Sunil Chandran; Joseph Cheriyan

doi:10.1016/j.orl.2018.09.002

paper

On Eulerian orientations of even-degree hypercubes

arXiv:1809.08507 · doi:10.1016/j.orl.2018.09.002

Abstract

It is well known that \textit{every} Eulerian orientation of an Eulerian $2 k$ -edge connected (undirected) graph is strongly $k$ -edge connected. An important goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity and element connectivity. We show that \textit{every} Eulerian orientation of the hypercube of degree $2 k$ is strongly $k$ -node connected.