Symmetric Graphs have symmetric Matchings
Group Theory
2016-07-26 v1
Abstract
Assume that there is a free group action of automorphisms on a bipartite graph. If there is a perfect matching on the factor graph, then obviously there is a perfect matching on the graph. Surprisingly, the reversed is also true for amenable groups: if there is a perfect matching on the graph, there is also a perfect matching on the factor graph, i. e. a group invariant ("symmetric") perfect matching on the graph.
Keywords
Cite
@article{arxiv.1607.07426,
title = {Symmetric Graphs have symmetric Matchings},
author = {Jan Fricke},
journal= {arXiv preprint arXiv:1607.07426},
year = {2016}
}