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arXiv · 0803.0864

An upper bound for the number of perfect matchings in graphs

Shmuel Friedland
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Abstract

We give an upper bound on the number of perfect matchings in an undirected simple graph $G$ with an even number of vertices, in terms of the degrees of all the vertices in $G$. This bound is sharp if $G$ is a union of complete bipartite graphs. This bound is a generalization of the upper bound on the number of perfect matchings in bipartite graphs on $n+n$ vertices given by the Bregman-Minc inequality for the permanents of $(0,1)$ matrices.

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Shmuel Friedland. 2008-03-06. An upper bound for the number of perfect matchings in graphs. https://arxiv.org/abs/0803.0864

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