Approximate Schreier decorations and approximate Kőnig's line coloring Theorem

2021/10/05 by Jan Grebik, Grebik, Jan
Mathematics · Engineering · #Limits and Structures in Graph Theory #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2110.01914

Abstract

Following recent result of L. M. T' oth [arXiv:1906.03137] we show that every 2Δ-regular Borel graph G with a (not necessarily invariant) Borel probability measure admits approximate Schreier decoration. In fact, we show that both ingredients from the analogous statements for finite graphs have approximate counterparts in the measurable setting, i.e., approximate Kőnig's line coloring Theorem for Borel graphs without odd cycles and approximate balanced orientation for even degree Borel graphs.

Related

• Definable Kőnig theorems
• Invariant Schreier decorations of unimodular random networks
• Embedding Borel graphs into grids of asymptotically optimal dimension
• Kőnig's Line Coloring and Vizing's Theorems for Graphings
• Borel Edge Colorings for Finite Dimensional Groups