Baire Measurable Matchings in Non-Amenable Graphs
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.
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