Vertex coloring of comparability +ke and -ke graphs

F + ke and T - ke graphs are classes of graphs close to graphs in a graph class T. They are the classes of graphs obtained by adding or deleting at most k edges from a graph in T. 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-1e graphs is solved in polynomial time.