A tree representation for P4-sparse graphs
Discrete Applied Mathematics
Stability number of bull- and chair-free graphs
Discrete Applied Mathematics
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
A decomposition for a class of &parl0;P5,P5&parr0;- free graphs
Discrete Mathematics
Discrete Mathematics
Weighted parameters in (P5,&Pmacr;5)-free graphs
Discrete Applied Mathematics
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
New Graph Classes of Bounded Clique-Width
WG '02 Revised Papers from the 28th International Workshop on Graph-Theoretic Concepts in 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
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De Simone showed that prime bull- and chair-free graphs containing a co-diamond are either bipartite or an induced cycle of odd length at least five. Based on this result, we give a complete structural characterization of prime (bull,chair)-free graphs having stability number at least four as well as of (bull,chair,co-chair)-free graphs. This implies constant-bounded clique width for these graph classes which leads to linear time algorithms for some algorithmic problems. Moreover, we obtain a robust O(nm) time algorithm for the maximum weight stable set problem on bull- and chair-free graphs without testing whether the (arbitrary) input graph is bull- and chair-free. This improves previous results with respect to structural insight, robustness and time bounds.