On Eulerian orientations of even-degree hypercubes

It is well known that every Eulerian orientation of an Eulerian 2k-edge connected (undirected) graph is strongly k-edge connected. A long-standing goal in the area is to obtain analogous results for other types of connectivity, such as node connectivity. We show that every Eulerian orientation of the hypercube of degree 2k is strongly k-node connected.