Dominator Colorings in Some Classes of Graphs

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.