Bipartite graphs with a perfect matching and digraphs
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 -extendable bipartite graphs and -strong digraphs. We also study the relation among -extendable bipartite graphs, -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.
Cite
@article{arxiv.1011.4359,
title = {Bipartite graphs with a perfect matching and digraphs},
author = {Zan-Bo Zhang and Dingjun Lou},
journal= {arXiv preprint arXiv:1011.4359},
year = {2010}
}
Comments
2 figures, 7 pages. A short version of this paper is published in "Advances and applications in Discrete Mathematics". This version contains some interesting comparison between $k$-strong digraphs and $k$-extendable bigraphs, which is deleted in the published version