Borel edge colorings for finite-dimensional groups

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2024-08-04 DOI:10.1007/s11856-024-2640-y

Felix Weilacher

引用次数: 0

Abstract

We study the potential of Borel asymptotic dimension, a tool introduced recently in [2], to help produce Borel edge colorings of Schreier graphs generated by Borel group actions. We find that it allows us to recover the classical bound of Vizing in certain cases, and also use it to exactly determine the Borel edge chromatic number for free actions of abelian groups.

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有限维群的玻尔边着色

我们研究了最近在[2]中引入的一种工具--玻尔渐近维度的潜力，它有助于产生由玻尔群作用生成的施赖尔图的玻尔边着色。我们发现它能让我们在某些情况下恢复 Vizing 的经典约束，还能用它精确地确定无性群自由作用的 Borel 边色度数。

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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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.