ON THE SECOND EIGENVALUE OF RANDOM REGULAR GRAPHS.

Andrei Broder*, Eli Shamir

*Corresponding author for this work

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

69 Scopus citations

Abstract

It is known that random d regular graphs are very efficient expanders, almost surely. However, checking whether a particular graph is a good expander is co-NP-complete. It is shown that the second eigenvalue of d-regular graphs, lambda //2, is concentrated in an interval of width O( ROOT d) around its mean, and that its mean is O(d**3**/**4). The result holds under various models for random d-regular graphs. As a consequence, a random d-regular graph on n vertices is, with high probability, a certifiable efficient expander for n sufficiently large. The bound on the width of the interval is derived from martingale theory, and the bound on E( lambda //2) is obtained by exploring the properties of random walks in random graphs.

Original languageEnglish
Title of host publicationAnnual Symposium on Foundations of Computer Science (Proceedings)
PublisherIEEE
Pages286-294
Number of pages9
ISBN (Print)0818608072, 9780818608070
DOIs
StatePublished - 1987
Externally publishedYes

Publication series

NameAnnual Symposium on Foundations of Computer Science (Proceedings)
ISSN (Print)0272-5428

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