Abstract
A dominator coloring is a coloring of the vertices of a graph such that every vertex is either alone in its color class or adjacent to all vertices of at least one other class. We present new bounds on the dominator coloring number of a graph, with applications to chordal graphs. We show how to compute the dominator coloring number in polynomial time for P 4-free graphs, and we give a polynomial-time characterization of graphs with dominator coloring number at most 3.
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This research was supported by French-Algerian program Tassili/CMEP number 05 MDU 639.
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Chellali, M., Maffray, F. Dominator Colorings in Some Classes of Graphs. Graphs and Combinatorics 28, 97–107 (2012). https://doi.org/10.1007/s00373-010-1012-z
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DOI: https://doi.org/10.1007/s00373-010-1012-z