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arXiv · 1011.4359

Bipartite graphs with a perfect matching and digraphs

Zan-Bo Zhang·Dingjun Lou
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Abstract

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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Zan-Bo Zhang, Dingjun Lou. 2010-11-19. Bipartite graphs with a perfect matching and digraphs. https://arxiv.org/abs/1011.4359

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