Every 4-colorable graph with maximum degree 4 has an equitable 4-coloring

H. A. Kierstead, A. V. Kostochka

Research output: Contribution to journalArticlepeer-review


Chen et al., conjectured that for r≥3, the only connected graphs with maximum degree at most r that are not equitably r-colorable are Kr, r (for odd r) and Kr + 1. If true, this would be a joint strengthening of the Hajnal-Szemerédi theorem and Brooks' theorem. Chen et al., proved that their conjecture holds for r = 3. In this article we study properties of the hypothetical minimum counter-examples to this conjecture and the structure of "optimal" colorings of such graphs. Using these properties and structure, we show that the Chen-Lih-Wu Conjecture holds for r≤4.

Original languageEnglish (US)
Pages (from-to)31-48
Number of pages18
JournalJournal of Graph Theory
Issue number1
StatePublished - Sep 2012


  • equitable coloring
  • maximum degree

ASJC Scopus subject areas

  • Geometry and Topology


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