Note on Halin's theorem on minimally connected graphs

Abstract In this note it is shown that any finite directed graph of strong connectivity n contains either a vertex with indegree n, a vertex with outdegree n, or an edge whose removal does not decrease the connectivity. This is a directed graph counterpart of Halin's theorem on undirected graphs. It is pointed out that only a few preparations and modifications are necessary to make his proof valid for directed graphs.