Bipartite graphs with a perfect matching and digraphs

Details Bipartite graphs with a perfect matching and digraphs Bipartite graphs with a perfect matching and digraphs

2010-11-19

arxiv.org/abs/1011.4359v1

Advances and applications in discrete mathematics, Volume 3, Number 2, April 2009, 155-164

Mathematics

Combinatorics

2 figures, 7 pages. A short version of this paper is published in "Advances and applications in Discrete Mathematics". This ve

Scientific paper

In this paper, we introduce a corresponding between bipartite graphs with a perfect matching and digraphs, which implicates an equivalent relation between the extendibility of bipartite graphs and the strongly connectivity of digraphs. Such an equivalent relation explains the similar results on $k$-extendable bipartite graphs and $k$-strong digraphs. We also study the relation among $k$-extendable bipartite graphs, $k$-strong digraphs and combinatorial matrices. For bipartite graphs that are not 1-extendable and digraphs that are not strong, we prove that the elementary components and strong components are counterparts.

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