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}
}