Ore-type versions of Brooks' theorem

Henry Kierstead, A. V. Kostochka

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The Ore-degree of an edge xy in a graph G is the sum θ (x y) = d (x) + d (y) of the degrees of its ends. In this paper we discuss colorings and equitable colorings of graphs with bounded maximum Ore-degree, θ (G) = maxx y ∈ E (G) θ (x y). We prove a Brooks-type bound on chromatic number of graphs G with θ (G) ≥ 12. We also discuss equitable and nearly equitable colorings of graphs with bounded maximum Ore-degree: we characterize r-colorable graphs with maximum Ore-degree at most 2r whose every r-coloring is equitable. Based on this characterization, we pose a conjecture on equitable r-colorings of graphs with maximum Ore-degree at most 2r, which extends the Chen-Lih-Wu Conjecture and one of our earlier conjectures. We prove that our conjecture is true for r = 3.

Original languageEnglish (US)
Pages (from-to)298-305
Number of pages8
JournalJournal of Combinatorial Theory. Series B
Issue number2
StatePublished - Mar 2009


  • Brooks' theorem
  • Edge degree
  • Equitable coloring
  • Graph coloring

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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