Vertex coloring of comparability+ke and -ke

Authors:
Yasuhiko Takenaga;Kenichi Higashide
Affiliations:
The University of Electro-Communications, Tokyo, Japan;The University of Electro-Communications, Tokyo, Japan
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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Abstract

e and e graphs are classes of graphs close to graphs in a graph class . They are the classes of graphs obtained by adding or deleting at most k edges from a graph in . 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.