On the number of edge disjoint cliques in graphs of given size

In this paper, we prove that any graph ofn vertices andt_r–1(n)+m edges, wheret_r–1(n) is the Turán number, contains (1–o(1)m edge disjointK_r'sifm=o(n²). Furthermore, we determine the maximumm such that every graph ofn vertices andt_r–1(n)+m edges containsm edge disjointK_r's ifn is sufficiently large.Research partially supported by Hungarian National Foundation for Scientific Research Grant no. 1812.