Vertex Coloring of Comparability+ke and –ke Graphs

Abstract

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