Year: 2012
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Csoka, Endre, Lippner, Gabor
Institutions: Eötvös Loránd University, Harvard University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1697928289