Minimal n-fach zusammenhängende Digraphen

AbstractFor a minimally n-connected digraph D, the subgraph spanned by the edges (x, y) with outdegree of x and indegree of y exceeding n is denoted by D0. It is proved that D0 corresponds to a forest. This implies that in a finite, minimally n-connected digraph D, the number of vertices of outdegree n is at least n and that the number of vertices of outdegree or indegree equal to n grows linearly in |D|. For almost every integer m, the maximum number of edges in a minimally n-connected digraph of order m is determined and the extremal digraphs are characterized