Measurable Regular Subgraphs

Fuente: arXiv
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Bibliographic Details
Main Authors: Bowen, Matt, Conley, Clinton T., Weilacher, Felix
Format: Preprint
Published: 2024
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author Bowen, Matt
Conley, Clinton T.
Weilacher, Felix
author_facet Bowen, Matt
Conley, Clinton T.
Weilacher, Felix
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_09597
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Measurable Regular Subgraphs
Bowen, Matt
Conley, Clinton T.
Weilacher, Felix
Logic
Combinatorics
03E15, 05C70
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.
title Measurable Regular Subgraphs
topic Logic
Combinatorics
03E15, 05C70
url https://arxiv.org/abs/2408.09597