Minimum Weighted Clique Cover on Strip-Composed Perfect Graphs
نویسندگان
چکیده
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 G, can be found in polynomial time, provided that the mwcc problem can be solved on G in polynomial time. We also design a new, more efficient, combinatorial algorithm for the mwcc problem on strip-composed claw-free perfect
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