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arXiv · 2501.07352

Borel fractional perfect matchings in quasi-transitive amenable graphs

Sam Murray
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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. 2025-01-13. Borel fractional perfect matchings in quasi-transitive amenable graphs. https://arxiv.org/abs/2501.07352

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