An Ore-type Theorem for Perfect Packings in Graphs
Daniela Kühn, Deryk Osthus, Andrew Treglown · SIAM Journal on Discrete Mathematics · 2009
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 nonadjacent $x ot=y\in V(G)$ contains a perfect H-packing. We determine $\lim_{n\to\infty}\delta_{\rm Ore}(H,n)/n$.