A Multipartite Hajnal-Szemerédi Theorem

Peter Keevash, Richard Mycroft

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
165 Downloads (Pure)


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.
Original languageEnglish
Pages (from-to)187-236
Number of pages50
JournalJournal of Combinatorial Theory. Series B
Early online date24 Apr 2015
Publication statusPublished - Sept 2015


  • graph theory
  • perfect packing


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