Borel fractional perfect matchings in quasi-transitive amenable graphs
Logic
2025-01-16 v2 Combinatorics
Abstract
We show that if a locally finite Borel graph with quasitransitive amenable components admits a fractional perfect matching, it will admit a Borel fractional perfect matching. In particular, if a countable amenable quasitransitive graph admits a fractional perfect matching then its Bernoulli graph admits a Borel fractional perfect matching.
Keywords
Cite
@article{arxiv.2501.07352,
title = {Borel fractional perfect matchings in quasi-transitive amenable graphs},
author = {Sam Murray},
journal= {arXiv preprint arXiv:2501.07352},
year = {2025}
}
Comments
18 pages, 5 figures; corrected reference