A Multipartite Hajnal-Szemerédi Theorem

Research output: Contribution to journalArticlepeer-review


Colleges, School and Institutes

External organisations

  • Mathematical Institute, University of Oxford


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 - Sep 2015


  • graph theory, perfect packing