On perfect packings in dense graphs
Abstract
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect H-packings: Given positive integers n, r, D, we characterise the edge density threshold that ensures a perfect K_r-packing in any graph G on n vertices and with minimum degree at least D. We also give two conjectures concerning degree sequence conditions which force a graph to contain a perfect H-packing. Other related embedding problems are also considered. Indeed, we give a structural result concerning K_r-free graphs that satisfy a certain degree sequence condition.
Keywords
Cite
@article{arxiv.1110.3490,
title = {On perfect packings in dense graphs},
author = {József Balogh and Alexandr V. Kostochka and Andrew Treglown},
journal= {arXiv preprint arXiv:1110.3490},
year = {2013}
}
Comments
18 pages, 1 figure. Electronic Journal of Combinatorics 20(1) (2013) #P57. This version contains an open problem section