Equivalence of two conjectures on equitable coloring of graphs

Bor-Liang Chen (), Ko-Wei Lih () and Chih-Hung Yen ()
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Bor-Liang Chen: National Taichung Institute of Technology
Ko-Wei Lih: Academia Sinica
Chih-Hung Yen: National Chiayi University

Journal of Combinatorial Optimization, 2013, vol. 25, issue 4, No 2, 504 pages

Abstract: 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.

Keywords: Equitable coloring; Maximum coloring; r-equitable graph; Maximum degree; Independence number (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-011-9429-8

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