, Volume 30, Issue 2, pp 217–224 | Cite as

A fast algorithm for equitable coloring

  • Henry A. KiersteadEmail author
  • Alexandr V. Kostochka
  • Marcelo Mydlarz
  • Endre Szemerédi


A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn 2) time, where n is the number of vertices.

Mathematics Subject Classification (2000)

05C15 05C85 


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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2010

Authors and Affiliations

  • Henry A. Kierstead
    • 1
    Email author
  • Alexandr V. Kostochka
    • 2
    • 3
  • Marcelo Mydlarz
    • 4
  • Endre Szemerédi
    • 5
  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA
  3. 3.Sobolev Institute of MathematicsNovosibirskRussia
  4. 4.Yahoo! Research Latin AmericaSantiagoChile
  5. 5.Department of Computer ScienceRutgers UniversityPiscatawayUSA

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