Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
Graph classes: a survey
Efficient and practical modular decomposition
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Linear-time modular decomposition and efficient transitive orientation of comparability graphs
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Structure and stability number of chair-, co-P- and gem-free graphs revisited
Information Processing Letters
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
Clique-width for four-vertex forbidden subgraphs
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
New applications of clique separator decomposition for the maximum weight stable set problem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Polynomial-time recognition of clique-width ≤3 graphs
Discrete Applied Mathematics
| Hi-index | 0.89 |
Minty has shown that the Maximum Weight Stable Set (MWS) Problem can be solved in polynomial time when restricted to claw-free graphs. We show that the structure of graphs being both claw-free and co-claw-free is very simple which implies bounded clique width for this graph class. It is known that for graph classes of bounded clique width (assuming that k- expressions can be determined in linear time), there are linear time algorithms for all problems expressible in Monadic Second Order Logic with quantification only over vertex sets. The problems MWS, Maximum Clique, Domination and Steiner Tree, for example, are expressible in this way.Moreover, we describe the structure of prime graphs being both H- and H-free for any four-vertex graph H and obtain bounded clique width for these graph classes except the 2K2- and C4-free graphs.