Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - Combinatorial Optimization
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
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
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
Discrete Mathematics
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
Independent sets in extensions of 2K2-free graphs
Discrete Applied Mathematics
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
Recognition Algorithm for Diamond-Free Graphs
Informatica
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Using the concept of prime graphs and modular decomposition of graphs, we give a complete structure description of (P5,diamond)-free graphs implying that these graphs have bounded clique width (the P5 is the induced path with five vertices a, b, c, d, e and four edges ab, bc, cd, de, and the diamond consists of four vertices a, b, c, d such that a, b, c form an induced path with edges ab, bc, and vertex d is adjacent to a,b and c). The structure and bounded clique width of this graph class allows to solve several algorithmic problems on this class in linear time, among them the problems Maximum Weight Stable Set (MWS), Maximum Weight Clique, Domination, Steiner Tree and in general every algorithmic problem which is, roughly speaking, expressible in a certain kind of Monadic Second-Order Logic using quantification only over vertex but not over edge set predicates. This improves previous results on (P5,diamond)-free graphs in several ways: We give a complete structure description of prime (P5,diamond)-free graphs, we do not only solve the MWS problem on this class, we achieve linear time algorithms (instead of a recent time bound O(nm)), and we can do all this on a larger graph class containing (P5,diamond)-free graphs which admits linear time recognition.