Sparse pseudo-random graphs are hamiltonian

Michael Krivelevich, Benny Sudakov

Research output: Contribution to journalArticlepeer-review

Abstract

In this article we study Hamilton cycles in sparse pseudorandom graphs. We prove that if the second largest absolute value λ of an eigenvalue of a d-regular graph G on n vertices satisfies λ ≤ (log log n)2/1000a log n (log log n) d and n is large enough, then G is Hamiltonian. We also show how out main result can be used to prove that for every c > 0 and large enough n a Cayley graph X(G,S), formed by choosing a set S of c log5 n random generators in a group G of order n, is almost surely Hamiltonian.

Original languageEnglish
Pages (from-to)17-33
Number of pages17
JournalJournal of Graph Theory
Volume42
Issue number1
DOIs
StatePublished - Jan 2003

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