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Sublinear Expanders and Their Applications

Published online by Cambridge University Press:  23 May 2024

By
Shoham Letzter
Edited by
Felix Fischer  and
Robert Johnson
Felix Fischer
Affiliation:
Queen Mary University of London
Robert Johnson
Affiliation:
Queen Mary University of London
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Summary

In this survey we aim to give a comprehensive overview of results using sublinear expanders. The term sublinear expanders refers to a variety of definitions of expanders, which typically are defined to be graphs G such that every not-too-small and not-too-large set of vertices U has neighbourhood of size at least α|U|, where α is a function of n and |U|. This is in contrast with linear expanders, where α is typically a constant. We will briefly describe proof ideas of some of the results mentioned here, as well as related open problems.

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Surveys in Combinatorics 2024 , pp. 89 - 130
Publisher: Cambridge University Press
Print publication year: 2024

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