Author:
Alon Noga,Friedland Shmuel
Abstract
We show that the number of perfect matchings in a simple graph $G$ with an even number of vertices and degree sequence $d_1,d_2, \ldots ,d_n$ is at most $ \prod_{i=1}^n (d_i!)^{{1\over 2d_i}}$. This bound is sharp if and only if $G$ is a union of complete balanced bipartite graphs.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
21 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Almost all optimally coloured complete graphs contain a rainbow Hamilton path;Journal of Combinatorial Theory, Series B;2022-09
2. The Graphs of Stably Matchable Pairs;Graph-Theoretic Concepts in Computer Science;2021
3. Number of 1-Factorizations of Regular High-Degree Graphs;Combinatorica;2020-03-04
4. Statistical Matching Theory;Bolyai Society Mathematical Studies;2019
5. Anagram-Free Colourings of Graphs;Combinatorics, Probability and Computing;2017-08-08