The maximum number of perfect matchings in graphs with a given degree sequence

Details The maximum number of perfect matchings in graphs with a given degree sequence The maximum number of perfect matchings in graphs with a given degree sequence

2008-03-18

arxiv.org/abs/0803.2578v2

Mathematics

Combinatorics

2 pages

Scientific paper

We show that the number of perfect matching in a simple graph $G$ with an
even number of vertices and degree sequence $d_1,d_2, ..., d_n$ is at most
$\prod_{i=1}^n (d_i !)^{\frac{1}{2d_i}}$. This bound is sharp if and only if
$G$ is a union of complete balanced bipartite graphs.

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