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EJC
2007

Perfect packings with complete graphs minus an edge

12 years 1 months ago
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.
Oliver Cooley, Daniela Kühn, Deryk Osthus
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where EJC
Authors Oliver Cooley, Daniela Kühn, Deryk Osthus
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