Expander graphs-both local and global

Michael Chapman, Nati Linial, Yuval Peled

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Let G=(V,E) be a finite graph. For v V we denote by G-v the subgraph of G that is induced by v's neighbor set. We say that G is (a,b)-regular for a>b>0 integers, if G is a-regular and G-v is b-regular for every v V. Recent advances in PCP theory call for the construction of infinitely many (a,b)-regular expander graphs G that are expanders also locally. Namely, all the graphs {G-v|v V} should be expanders as well. While random regular graphs are expanders with high probability, they almost surely fail to expand locally. Here we construct two families of (a,b)-regular graphs that expand both locally and globally. We also analyze the possible local and global spectral gaps of (a,b)-regular graphs. In addition, we examine our constructions vis-A-vis properties which are considered characteristic of high-dimensional expanders.

Original languageAmerican English
Title of host publicationProceedings - 2019 IEEE 60th Annual Symposium on Foundations of Computer Science, FOCS 2019
PublisherIEEE Computer Society
Pages158-170
Number of pages13
ISBN (Electronic)9781728149523
DOIs
StatePublished - Nov 2019
Event60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019 - Baltimore, United States
Duration: 9 Nov 201912 Nov 2019

Publication series

NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
Volume2019-November
ISSN (Print)0272-5428

Conference

Conference60th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2019
Country/TerritoryUnited States
CityBaltimore
Period9/11/1912/11/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Keywords

  • Expander-Graphs
  • High-dimensional Combinatorics

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