A fast algorithm for equitable coloring

Henry Kierstead, Alexandr V. Kostochka, Marcelo Mydlarz, Endre Szemerédi

Research output: Contribution to journalArticle

37 Scopus citations


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(rn2) time, where n is the number of vertices.

Original languageEnglish (US)
Pages (from-to)217-224
Number of pages8
Issue number2
StatePublished - Sep 28 2010


ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

Cite this

Kierstead, H., Kostochka, A. V., Mydlarz, M., & Szemerédi, E. (2010). A fast algorithm for equitable coloring. Combinatorica, 30(2), 217-224. https://doi.org/10.1007/s00493-010-2483-5