### 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 language | English (US) |
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Pages (from-to) | 226-234 |

Number of pages | 9 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 98 |

Issue number | 1 |

DOIs | |

State | Published - 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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## Cite this

Kierstead, H., & Kostochka, A. V. (2008). An Ore-type theorem on equitable coloring.

*Journal of Combinatorial Theory. Series B*,*98*(1), 226-234. https://doi.org/10.1016/j.jctb.2007.07.003