A Multipartite Hajnal-Szemer\'edi Theorem
Combinatorics
2015-09-15 v2
Abstract
The celebrated Hajnal-Szemer\'edi theorem gives the precise minimum degree threshold that forces a graph to contain a perfect K_k-packing. Fischer's conjecture states that the analogous result holds for all multipartite graphs except for those formed by a single construction. Recently, we deduced an approximate version of this conjecture from new results on perfect matchings in hypergraphs. In this paper, we apply a stability analysis to the extremal cases of this argument, thus showing that the exact conjecture holds for any sufficiently large graph.
Cite
@article{arxiv.1201.1882,
title = {A Multipartite Hajnal-Szemer\'edi Theorem},
author = {Peter Keevash and Richard Mycroft},
journal= {arXiv preprint arXiv:1201.1882},
year = {2015}
}
Comments
Final version, accepted to appear in JCTB. 43 pages, 2 figures