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Minimal n-fach zusammenhängende Digraphen. (Minimally n-connected digraphs). (German) Zbl 0578.05045
The author has proved [Arch. Math. 23, 219-224 (1972; Zbl 0212.294), 553-560 (1972; Zbl 0228.05119)] that in an undirected minimally n- connected graph the subgraph spanned by the vertices of degree greater than n corresponds to a forest. In this article he examines the directed case and proves that in each minimally n-connected digraph, the subgraph spanned by the edges (x,y) with outdegree of X and indegree of Y exceeding n contains no alternating cycle. Therefore this subgraph corresponds to a forest. From this he deduces some theorems on the maximum number of edges in minimally n-connected graphs and characterizes extremal digraphs.
Reviewer: M.Hager

05C40 Connectivity
05C20 Directed graphs (digraphs), tournaments
05C35 Extremal problems in graph theory
Full Text: DOI
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