Borel edge colorings for finite-dimensional groups
摘要
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.