Clique-factors in sparse pseudorandom graphs. (December 2019) - Han, Jie; Kohayakawa, Yoshiharu; Morris, Patrick; Person, Yury
Abstract: We prove that for any t ≥ 3 there exist constants c > 0 and   n 0 such that any d -regular n -vertex graph  G with t ∣ n ≥ n 0 and second largest eigenvalue in absolute value  λ satisfying λ ≤ c d t ∕ n t − 1 contains a K t -factor, that is, vertex-disjoint copies of K t covering every vertex of  G . The result generalizes to broader setting of jumbled graphs, which were introduced by Thomason in the eighties.