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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可测量的正则子图
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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