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arXiv · 0803.2578

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

Noga Alon·Shmuel Friedland
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Abstract

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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Noga Alon, Shmuel Friedland. 2008-05-26. The maximum number of perfect matchings in graphs with a given degree sequence. https://arxiv.org/abs/0803.2578

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