Packing edge disjoint cliques in graphs

Abstract

Let $r\ge 3$ be fixed and $G$ be an $n$-vertex graph. A long-standing conjecture of Győri states that if $e(G)=t_{r-1}(n)+k$, where $t_{r-1}(n)$ denotes the number of edges of the Turán graph on $n$ vertices and $r-1$ parts, then $G$ has at least $(2-o(1))k/r$ edge disjoint $r$-cliques. We prove this conjecture.

Updated with referees' suggestions