Baire Measurable Matchings in Non-Amenable Graphs

Alexander Kastner; Clark Lyons

Baire Measurable Matchings in Non-Amenable Graphs

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arxiv 2310.20047 v2 pith:LGNZXFLS submitted 2023-10-30 math.LO

Alexander Kastner , Clark Lyons This is my paper · ORCID

classification math.LO

keywords bairemeasurablenon-amenableboreleverygraphonlyprove

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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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Spectral Theory for Borel PMP Graphs
math.LO 2026-02 accept novelty 7.0 of 10

Spectral theory of adjacency and Laplacian operators yields new optimal bounds on approximate measurable chromatic numbers of graphings and a spectral criterion for a measurable Tutte condition.

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