Minimum weighted clique cover on strip-composed perfect graphs

Abstract

The only available combinatorial algorithm for the minimum weighted clique cover (mwcc) in claw-free perfect graphs is due to Hsu and Nemhauser [10] and dates back to 1984. More recently, Chudnovsky and Seymour [3] introduced a composition operation, strip-composition, in order to define their structural results for claw-free graphs; however, this composition operation is general and applies to non-claw-free graphs as well. In this paper, we show that a mwcc of a perfect strip-composed graph, with the basic graphs belonging to a class, can be found in polynomial time, provided that the mwcc problem can be solved on in polynomial time. We also design a new, more efficient, combinatorial algorithm for the mwcc problem on strip-composed claw-free perfect graphs. © 2012 Springer-Verlag Berlin Heidelberg.