Elsevier

Discrete Mathematics

Volume 311, Issue 13, 6 July 2011, Pages 1158-1163
Discrete Mathematics

Maximal independent sets in minimum colorings

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Abstract

Every graph G contains a minimum vertex-coloring with the property that at least one color class of the coloring is a maximal independent set (equivalently, a dominating set) in G. Among all such minimum vertex-colorings of the vertices of G, a coloring with the maximum number of color classes that are dominating sets in G is called a dominating-χ-coloring of G. The number of color classes that are dominating sets in a dominating-χ-coloring of G is defined to be the dominating-χ-color number of G. In this paper, we continue to investigate the dominating-χ-color number of a graph first defined and studied in [1].

Keywords

Coloring
Chromatic number
Domination number
Maximal independent set
Dominating-χ-color number
Dom-color number

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