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Equivalence of two conjectures on equitable coloring of graphs |
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| Authors: | Bor-Liang Chen Ko-Wei Lih Chih-Hung Yen |
| Affiliation: | 1. Department of Business Administration, National Taichung Institute of Technology, Taichung, 40401, Taiwan 2. Institute of Mathematics, Academia Sinica, Taipei, 10617, Taiwan 3. Department of Applied Mathematics, National Chiayi University, Chiayi, 60004, Taiwan |
| 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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