Remarks on partitions into expanders
Combinatorics
2021-01-13 v2 Metric Geometry
Abstract
In this note we give a short proof that graphs having no linearly small F{\o}lner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for graphs admitting linearly small maximal F{\o}lner sets and we deduce that a family of such graphs must contain a family of expanders. We also show that the existence of partitions into expanders is a quasi-isometry invariant.
Cite
@article{arxiv.2001.01522,
title = {Remarks on partitions into expanders},
author = {Federico Vigolo},
journal= {arXiv preprint arXiv:2001.01522},
year = {2021}
}
Comments
7 pages. Lemma 3.1 has been corrected. Various minor changes throughout