Clique-factors in sparse pseudorandom graphs

Abstract

We prove that for any t≥3 there exist constants c>0 and n0 such that any d-regular n-vertex graph G with t∣n≥n0 and second largest eigenvalue in absolute value λ satisfying λ≤cdt∕nt−1 contains a Kt-factor, that is, vertex-disjoint copies of Kt covering every vertex of G. The result generalizes to broader setting of jumbled graphs, which were introduced by Thomason in the eighties.