A short proof of the Hajnal-Szemerédi theorem on equitable colouring

Henry Kierstead, A. V. Kostochka

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


A proper vertex colouring of a graph is equitable if the sizes of colour classes differ by at most one. We present a new shorter proof of the celebrated Hajnal-Szemerédi theorem: for every positive integer r, every graph with maximum degree at most r has an equitable colouring with r + 1 colours. The proof yields a polynomial time algorithm for such colourings.

Original languageEnglish (US)
Pages (from-to)265-270
Number of pages6
JournalCombinatorics Probability and Computing
Issue number2
StatePublished - Mar 2008

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Computational Theory and Mathematics
  • Applied Mathematics


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