Turán numbers of vertex-disjoint cliques in r-partite graphs

For two graphs G and H, the Turán numberex(G,H) is the maximum number of edges in a subgraph of G that contains no copy of H. Chen, Li, and Tu determined the Turán numbers ex(Km,n,kK2) for all k≥1 Chen et al. (2009). In this paper we will determine the Turán numbers ex(Ka1,…,ar,kKr) for all r≥3 and k≥1.