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Equivalence of two conjectures on equitable coloring of graphs

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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.

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Authors and Affiliations

  1. Department of Business Administration, National Taichung Institute of Technology, Taichung, 40401, Taiwan

    Bor-Liang Chen

  2. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan

    Ko-Wei Lih

  3. Department of Applied Mathematics, National Chiayi University, Chiayi, 60004, Taiwan

    Chih-Hung Yen

Authors
  1. Bor-Liang Chen
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  2. Ko-Wei Lih
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  3. Chih-Hung Yen
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Correspondence to Chih-Hung Yen.

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Chen, BL., Lih, KW. & Yen, CH. Equivalence of two conjectures on equitable coloring of graphs. J Comb Optim 25, 501–504 (2013). https://doi.org/10.1007/s10878-011-9429-8

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  • DOI: https://doi.org/10.1007/s10878-011-9429-8

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