An Ore-type theorem for perfect packings in graphs
Combinatorics
2009-06-02 v2
Abstract
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.
Cite
@article{arxiv.0807.4907,
title = {An Ore-type theorem for perfect packings in graphs},
author = {Daniela Kühn and Deryk Osthus and Andrew Treglown},
journal= {arXiv preprint arXiv:0807.4907},
year = {2009}
}
Comments
23 pages, 1 figure. Extra examples and a sketch proof of Theorem 4 added. To appear in the SIAM Journal on Discrete Mathematics