Article

# A Multipartite Hajnal-Szemer\'edi Theorem

01/2012;
Source: arXiv

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.

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