Borel fractional perfect matchings in quasi-transitive amenable graphs

Published 13 Jan 2025 in math.LO and math.CO | (2501.07352v2)

Abstract: We show that if a locally finite Borel graph with quasitransitive amenable components admits a fractional perfect matching, it will admit a Borel fractional perfect matching. In particular, if a countable amenable quasitransitive graph admits a fractional perfect matching then its Bernoulli graph admits a Borel fractional perfect matching.

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Sam Murray

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