Measurable Regular Subgraphs
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.09597
- arXiv:
- arXiv:2408.09597
- Bibcode:
- 2024arXiv240809597B
- Keywords:
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- Mathematics - Logic;
- Mathematics - Combinatorics;
- 03E15;
- 05C70