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Equivalence of two conjectures on equitable coloring of graphs

Author

Listed:
  • Bor-Liang Chen

    (National Taichung Institute of Technology)

  • Ko-Wei Lih

    (Academia Sinica)

  • Chih-Hung Yen

    (National Chiayi University)

Abstract

A graph G is said to be equitably k-colorable if there exists a proper k-coloring of G such that the sizes of any two color classes differ by at most one. Let Δ(G) denote the maximum degree of a vertex in G. Two Brooks-type conjectures on equitable Δ(G)-colorability have been proposed in Chen and Yen (Discrete Math., 2011) and Kierstead and Kostochka (Combinatorica 30:201–216, 2010) independently. We prove the equivalence of these conjectures.

Suggested Citation

  • Bor-Liang Chen & Ko-Wei Lih & Chih-Hung Yen, 2013. "Equivalence of two conjectures on equitable coloring of graphs," Journal of Combinatorial Optimization, Springer, vol. 25(4), pages 501-504, May.
    • Handle: RePEc:spr:jcomop:v:25:y:2013:i:4:d:10.1007_s10878-011-9429-8
    DOI: 10.1007/s10878-011-9429-8
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    Cited by:

    1. Shasha Ma & Liancui Zuo, 2016. "Equitable colorings of Cartesian products of square of cycles and paths with complete bipartite graphs," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 725-740, October.

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