Vertex coloring of comparability +ke and -ke graphs

Abstract

F + ke and F - ke graphs are classes ofgraphs close to graphs in a graph class F. They are the classes of graphs obtained by adding or deleting at most k edges from a graph in F. In this paper, we consider vertex coloring of comparability+ke and comparability-ke graphs. We show that for comparability+ke graphs, vertex coloring is solved in polynomial time for k = 1 and NP-complete for k ≥ 2. We also show that vertex coloring of comparability-le graphs is solved in polynomial time. © Springer-Verlag Berlin Heidelberg 2006.