A short proof of the hajnal–szemerédi theorem on equitable colouring

  • Authors:

  • H. a. Kierstead;A. v. Kostochka

  • Affiliations:

  • Department of mathematics and statistics, arizona state university, tempe, az 85287, usa (e-mail: kierstead@asu.edu);Department of mathematics, university of illinois, urbana, il 61801, usa and institute of mathematics, novosibirsk, 630090, russia (e-mail: kostochk@math.uiuc.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2008

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Abstract

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.