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arXiv · 2408.09597

Measurable Regular Subgraphs

Matt Bowen·Clinton T. Conley·Felix Weilacher
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Abstract

We show that every $d$-regular bipartite Borel graph admits a Baire measurable $k$-regular spanning subgraph if and only if $d$ is odd or $k$ is even. This gives the first example of a locally checkable coloring problem which is known to have a Baire measurable solution on Borel graphs but not a computable solution on highly computable graphs. We also prove the analogous result in the measure setting for hyperfinite graphs.

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Matt Bowen, Clinton T. Conley, Felix Weilacher. 2024-08-18. Measurable Regular Subgraphs. https://arxiv.org/abs/2408.09597

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