Some remarks on Arc‐connectivity, vertex splitting, and orientation in graphs and digraphs
Bill Jackson · Journal of Graph Theory · 1988
Abstract We apply proof techniques developed by L. Lovász and A. Frank to obtain several results on the arc‐connectivity of graphs and digraphs. The first results concern the operation of splitting two arcs from a vertex of an Eulerian graph or digraph in such a way as to preserve local connectivity conditions. The final result is concerned with orienting the edges of a mixed graph (consisting of vertices, undirected edges, and directed arcs) in such a way that the resulting digraph is as arc‐connected as possible.