An Ore-type theorem for perfect packings in graphs

Details An Ore-type theorem for perfect packings in graphs An Ore-type theorem for perfect packings in graphs

2008-07-30

arxiv.org/abs/0807.4907v2

Mathematics

Combinatorics

23 pages, 1 figure. Extra examples and a sketch proof of Theorem 4 added. To appear in the SIAM Journal on Discrete Mathematic

Scientific paper

We say that a graph G has a perfect H-packing (also called an H-factor) if there exists a set of disjoint copies of H in G which together cover all the vertices of G. Given a graph H, we determine, asymptotically, the Ore-type degree condition which ensures that a graph G has a perfect H-packing. More precisely, let \delta_{\rm Ore} (H,n) be the smallest number k such that every graph G whose order n is divisible by |H| and with d(x)+d(y)\geq k for all non-adjacent x \not = y \in V(G) contains a perfect H-packing. We determine \lim_{n\to \infty} \delta_{\rm Ore} (H,n)/n.

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