Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
On extendedP4-reducible and extendedP4-sparse graphs
Theoretical Computer Science
Graph classes: a survey
Modular decomposition and transitive orientation
Discrete Mathematics - Special issue on partial ordered sets
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Conic reduction of graphs for the stable set problem
Discrete Mathematics
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Information Processing Letters
New Graph Classes of Bounded Clique-Width
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in Computer Science
A New Linear Algorithm for Modular Decomposition
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
On the structure and stability number of P5- and co-chair-free graphs
Discrete Applied Mathematics - Special issue on stability in graphs and related topics
Efficient robust algorithms for the maximum weight stable set problem in chair-free graph classes
Information Processing Letters
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
Journal of Discrete Algorithms
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 |
The P4 is the induced path with vertices a, b, c, d and edges ab, bc, cd. The chair (co-P, gem) has a fifth vertex adjacent to b (a and b, a, b, c and d, respectively). We give a complete structure description of prime chair-, co-P- and gem-free graphs which implies bounded clique width for this graph class. It is known that this has some nice consequences; very roughly speaking, every problem expressible in a certain kind of Monadic Second Order Logic (quantifying only over vertex set predicates) can be solved efficiently for graphs of bounded clique width. In particular, we obtain linear time for the problems Vertex Cover, Maximum Weight Stable Set (MWS), Maximum Weight Clique, Steiner Tree, Domination and Maximum Induced Matching on chair-, co-P- and gem-free graphs and a slightly larger class of graphs. This drastically improves a recently published O(n4) time bound for Maximum Stable Set on butterfly-, chair-, co-P- and gem-free graphs.