Factorially Many Maximum Matchings Close to the Erdős-Gallai Bound
-
Published:2022-06-17
Issue:2
Volume:29
Page:
-
ISSN:1077-8926
-
Container-title:The Electronic Journal of Combinatorics
-
language:
-
Short-container-title:Electron. J. Combin.
Author:
Bessy Stéphane,Pardey Johannes,Picasarri-Arrieta Lucas,Rautenbach Dieter
Abstract
A classical result of Erdős and Gallai determines the maximum size $m(n,\nu)$ of a graph $G$ of order $n$ and matching number $\nu n$. We show that $G$ has factorially many maximum matchings provided that its size is sufficiently close to $m(n,\nu)$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics