Perfect packings with complete graphs minus an edge

Let denote the graph obtained from K_r by deleting one edge. We show that for every integer r≥4 there exists an integer n₀=n₀(r) such that every graph G whose order n≥n₀ is divisible by r and whose minimum degree is at least contains a perfect -packing, i.e. a collection of disjoint copies of which covers all vertices of G. Here is the critical chromatic number of . The bound on the minimum degree is best possible and confirms a conjecture of Kawarabayashi for large n.