Perfect packings with complete graphs minus an edge

Let K− r denote the graph obtained from Kr 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 (1−1/χcr(K− r ))n contains a perfect K− r -packing, i.e. a collection of disjoint copies of K− r which covers all vertices of G. Here χcr(K− r ) = r(r−2) r−1 is the critical chromatic number of K− r . The bound on the minimum degree is best possible and confirms a conjecture of Kawarabayashi for large n.

• Type: Journal
• Year: 2007
• Where: EJC
• Authors: Oliver Cooley, Daniela Kühn, Deryk Osthus
• Keywords: Disjoint Copies, EJC 2007, Information Technology, Integer, Minimum Degree