Baire Measurable Matchings in Non-Amenable Graphs

Alexander Kastner; Clark Lyons

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arXiv · 2310.20047

Baire Measurable Matchings in Non-Amenable Graphs

Alexander Kastner·Clark Lyons

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Abstract

We prove that every Schreier graph of a free Borel action of a finitely generated non-amenable group admits a Baire measurable perfect matching, and that the Schreier graph of a free computable action of a finitely generated non-amenable group admits a computable perfect matching. These results were previously only known in the bipartite setting. To prove them, we establish variants of Tutte's theorem on perfect matchings in non-bipartite graphs. We also prove that every Borel non-amenable bounded-degree graph with only even degrees admits a Baire measurable balanced orientation.

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BibTeX RIS

Alexander Kastner, Clark Lyons. 2023-10-30. Baire Measurable Matchings in Non-Amenable Graphs. https://arxiv.org/abs/2310.20047

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