Stability number of bull- and chair-free graphs
Discrete Applied Mathematics
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Structure and stability number of chair-, co-P- and gem-free graphs revisited
Information Processing Letters
Stability number of bull- and chair-free graphs revisited
Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Polynomial algorithm for finding the largest independent sets in graphs without forks
Discrete Applied Mathematics
Efficient robust algorithms for the maximum weight stable set problem in chair-free graph classes
Information Processing Letters
Maximum independent sets in graphs of low degree
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The Maximum Independent Set Problem in Planar Graphs
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Maximum independent sets in subclasses of P5-free graphs
Information Processing Letters
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
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The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum weight independent set problem in the class of line graphs, which is equivalent to the maximum matching problem in general graphs, has been proposed by Edmonds in 1965 and then extended to the entire class of claw-free graphs by Minty in 1980. Recently, Alekseev proposed a solution for the larger class of fork-free graphs, but only for the unweighted version of the problem, i.e. finding an independent set of maximum cardinality. In the present paper, we describe the first polynomial-time algorithm to solve the problem for weighted fork-free graphs.