English

Baire Measurable Matchings in Non-Amenable Graphs

Logic 2023-11-14 v2

Abstract

We prove that every Schreier graph of a free Borel action of a finitely generated non-amenable group has a Baire measurable perfect matching. This result was previously only known in the bipartite setting. We also prove that every Borel non-amenable bounded degree graph with only even degrees has a Baire measurable balanced orientation.

Cite

@article{arxiv.2310.20047,
  title  = {Baire Measurable Matchings in Non-Amenable Graphs},
  author = {Alexander Kastner and Clark Lyons},
  journal= {arXiv preprint arXiv:2310.20047},
  year   = {2023}
}
R2 v1 2026-06-28T13:06:44.802Z