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arXiv · 1410.0246

A continuum of expanders

David Hume
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Abstract

A regular equivalence between two graphs $\Gamma,\Gamma'$ is a pair of uniformly proper Lipschitz maps $V\Gamma\to V\Gamma'$ and $V\Gamma'\to V\Gamma$. Using separation profiles we prove that there are $2^{\aleph_0}$ regular equivalence classes of expander graphs, and of finitely generated groups with a representative which isometrically contains expanders.

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David Hume. 2014-10-01. A continuum of expanders. https://arxiv.org/abs/1410.0246

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