English

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