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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Acknowledgements
The author was partially supported by the ARCS foundation, Pittsburgh chapter. He also thanks Clinton Conley for many helpful discussions. He is most indebted to the anonymous referee, whose thoughtful feedback helped greatly improve the presentation of this paper.
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Weilacher, F. Borel edge colorings for finite-dimensional groups. Isr. J. Math. (2024). https://doi.org/10.1007/s11856-024-2640-y
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DOI: https://doi.org/10.1007/s11856-024-2640-y