Invariant random matchings in Cayley graphs
Combinatorics
2012-11-13 v1 Dynamical Systems
Probability
Abstract
We prove that any non-amenable Cayley graph admits a factor of IID perfect matching. We also show that any connected d-regular vertex tran- sitive graph admits a perfect matching. The two results together imply that every Cayley graph admits an invariant random perfect matching. A key step in the proof is a result on graphings that also applies to finite graphs. The finite version says that for any partial matching of a finite regular graph that is a good expander, one can always find an augmenting path whose length is poly-logarithmic in one over the ratio of unmatched vertices.
Keywords
Cite
@article{arxiv.1211.2374,
title = {Invariant random matchings in Cayley graphs},
author = {Endre Csoka and Gabor Lippner},
journal= {arXiv preprint arXiv:1211.2374},
year = {2012}
}
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29 pages