可测量的正则子图

arXiv - MATH - Logic Pub Date : 2024-08-18 DOI:arxiv-2408.09597

Matt Bowen, Clinton T. Conley, Felix Weilacher

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引用次数: 0

摘要

我们证明，当且仅当 $d$ 为奇数或 $k$ 为偶数时，每个 $d$ 规则的双方波尔图都有一个可 Bairemeasurable $k$ 规则的跨子图。这给出了第一个局部可检验着色问题的例子，已知这个问题在伯尔图上有一个百里可测解，但在高度可计算图上没有一个可计算解。我们还证明了超无限图的度量设置中的类似结果。

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Measurable Regular Subgraphs

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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arXiv - MATH - Logic

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