Remarks on partitions into expanders
Abstract
In this note we give a short proof that graphs having no linearly small Flner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for graphs admitting linearly small maximal Flner 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.
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