An Ore-type theorem on equitable coloring

Henry Kierstead, A. V. Kostochka

Research output: Contribution to journalArticle

47 Scopus citations

Abstract

A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this paper, we prove that if G is a graph such that for each edge x y ∈ E (G), the sum d (x) + d (y) of the degrees of its ends is at most 2 r + 1, then G has an equitable coloring with r + 1 colors. This extends the Hajnal-Szemerédi Theorem on graphs with maximum degree r and a recent conjecture by Kostochka and Yu. We also pose an Ore-type version of the Chen-Lih-Wu Conjecture and prove a very partial case of it.

Original languageEnglish (US)
Pages (from-to)226-234
Number of pages9
JournalJournal of Combinatorial Theory. Series B
Volume98
Issue number1
DOIs
StatePublished - Jan 1 2008

Keywords

  • Equitable coloring
  • Ore-type
  • Packing

ASJC Scopus subject areas

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

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