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A fast algorithm for equitable coloring

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, P.O. Box 871804, Tempe, AZ, 85287, USA

    Henry A. Kierstead

  2. Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL, 61801, USA

    Alexandr V. Kostochka

  3. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    Alexandr V. Kostochka

  4. Yahoo! Research Latin America, Blanco Encalada 2120, 4h floor, Santiago, Chile

    Marcelo Mydlarz

  5. Department of Computer Science, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA

    Endre Szemerédi

Authors
  1. Henry A. Kierstead
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  2. Alexandr V. Kostochka
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  3. Marcelo Mydlarz
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  4. Endre Szemerédi
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Corresponding author

Correspondence to Henry A. Kierstead.

Additional information

Research of this author is supported in part by the NSA grant MDA 904-03-1-0007.

Research of this author is supported in part by NSF grant DMS-06-50784 and by grant 06-01-00694 of the Russian Foundation for Basic Research.

Research of this author is supported in part by NSF grant DMS-0902241.

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Kierstead, H.A., Kostochka, A.V., Mydlarz, M. et al. A fast algorithm for equitable coloring. Combinatorica 30, 217–224 (2010). https://doi.org/10.1007/s00493-010-2483-5

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  • DOI: https://doi.org/10.1007/s00493-010-2483-5

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