Turán number of two vertex-disjoint copies of cliques

Abstract

The Turán number of a given graph H, denoted by ex(n, H), is the maximum number of edges in an H-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(n, K_p ∪ K_q) of a vertex-disjoint union of cliques K_p and K_q for all values of n.