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On Vertices of outdegree n in minimally n-connected digraphs

✍ Scribed by W. Mader

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
202 KB
Volume
39
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

Let |D| and |D|^+^~n~ denote the number of vertices of D and the number of vertices of outdegree n in the digraph D, respectively. It is proved that every minimally n‐connected, finite digraph D has |D|^+^~n~ ≥ n + 1 and that for n ≥ 2, there is a c~n~ > 0 such that $|D|^+_n > C_n \sqrt{|D|}$ for all minimally n‐connected, finite digraphs D. Furthermore, case n = 2 of the following conjecture is settled which says that every minimally n‐connected, finite digraph has a vertex of indegree and outdegree equal to n. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 129–144, 2002

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