A Multipartite Hajnal-Szemerédi Theorem

Details A Multipartite Hajnal-Szemerédi Theorem A Multipartite Hajnal-Szemerédi Theorem

2012-01-09

arxiv.org/abs/1201.1882v1

Mathematics

Combinatorics

43 pages, 2 figures

Scientific paper

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.

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