Title: Erdös' conjecture on multiplicities of complete subgraphs for nearly quasirandom graphs

Let k_t(G) denote the number of cliques of order t in the graph G and let  c_t(G) be the ratio of (k_t(G) + k_t(G)) and the value C(t,|G|), where G denotes the complement graph of G and C(a,b) denotes the quantity a choose b. In simple terms, it is the ratio of t-cliques and cocliques and the number of t-subsets of G. Finally, let c_t(n) = min{ c_t(G) : |G| = n } and let c_t be the limit of c_t(n) for n approaching infinity.

An old conjecture of Erdös related to Ramsey's theorem states that c_t =2^1-C(t,2). It was shown false by A. Thomason. It has been known that c_t(G) must be approximatelly equal to c_t whenever G is a pseudorandom graph. The aim of this talk is to show that c₄(G) ≥ c₄ if G is a graph arising from a pseudorandom one by a small perturbation. Joint research with. V. Rödl.