Quasirandom Cayley graphs

Abstract

We prove that the properties of having small discrepancy and having small second eigenvalue are equivalent in Cayley graphs, extending a result of Kohayakawa, R\"odl, and Schacht, who treated the abelian case. The proof relies on Grothendieck's inequality. As a corollary, we also prove that a similar result holds in all vertex-transitive graphs.