A Multipartite Hajnal-Szemerédi Theorem
arXiv:1201.1882 · doi:10.1016/j.jctb.2015.04.003
Abstract
The celebrated Hajnal-Szemerédi 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.
Final version, accepted to appear in JCTB. 43 pages, 2 figures