Expander Graphs — Both Local and Global

Michael Chapman*, Nati Linial, Yuval Peled

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Let G = (V, E) be a finite graph. For v ∈ V we denote by Gv 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 Gv 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 {Gv ∣ 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
Pages (from-to)473-509
Number of pages37
Issue number4
StatePublished - 1 Aug 2020

Bibliographical note

Publisher Copyright:
© 2020, János Bolyai Mathematical Society and Springer-Verlag.


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