Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
The stable set polytope of quasi-line graphs
Combinatorica
A new algorithm for the maximum weighted stable set problem in claw-free graphs
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Domination when the stars are out
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Claw-free graphs. VII. Quasi-line graphs
Journal of Combinatorial Theory Series B
Minimum clique cover in claw-free perfect graphs and the weak Edmonds-Johnson property
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
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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 ${\cal G}$, can be found in polynomial time, provided that the mwcc problem can be solved on ${\cal G}$ in polynomial time. We also design a new, more efficient, combinatorial algorithm for the mwcc problem on strip-composed claw-free perfect graphs.