Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
A strengthening of Ben Rebea's lemma
Journal of Combinatorial Theory Series B
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On claw-free asteroidal triple-free graphs
Discrete Applied Mathematics
On linear and circular structure of (claw, net)-free graphs
Discrete Applied Mathematics
On clique separators, nearly chordal graphs, and the Maximum Weight Stable Set Problem
Theoretical Computer Science
Claw-free graphs. V. Global structure
Journal of Combinatorial Theory Series B
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
Claw-free graphs and two conjectures on omega, delta, and chi
Claw-free graphs and two conjectures on omega, delta, and chi
Domination when the stars are out
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Parameterized complexity of induced h-matching on claw-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Triangulation and clique separator decomposition of claw-free graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Minimum weighted clique cover on strip-composed perfect graphs
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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
Efficient recognition of equimatchable graphs
Information Processing Letters
A reduction algorithm for the weighted stable set problem in claw-free graphs
Discrete Applied Mathematics
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We propose an algorithm for solving the maximum weighted stable set problem on claw-free graphs that runs in O(n3)--time, drastically improving the previous best known complexity bound. This algorithm is based on a novel decomposition theorem for claw-free graphs, which is also introduced in the present paper. Despite being weaker than the well-known structure result for claw-free graphs given by Chudnovsky and Seymour [5], our decomposition theorem is, on the other hand, algorithmic, i.e. it is coupled with an O(n3)-time procedure that actually produces the decomposition. We also believe that our algorithmic decomposition result is interesting on its own and might be also useful to solve other kind of problems on claw-free graphs.