Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - Computational combinatiorics
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
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
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
On the Relationship between Clique-Width and Treewidth
WG '01 Proceedings of the 27th 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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On algorithms for (P5,gem)-free graphs
Theoretical Computer Science - Graph colorings
New applications of clique separator decomposition for the Maximum Weight Stable Set problem
Theoretical Computer Science
Recent developments on graphs of bounded clique-width
Discrete Applied Mathematics
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It is well known that the clique-width of chordal gem-free graphs (also known as ptolemaic graphs), as a subclass of distancehereditary graphs, is at most 3. Hereby, the gem consists of a P4 plus a vertex being completely adjacent to the P4, and the co-gem is its complement graph. On the other hand, unit interval graphs being another important subclass of chordal graphs, have unbounded clique-width. In this note, we show that, based on certain tree structure and module properties, chordal co-gem-free graphs have clique-width at most eight. By a structure result for (P5, gem)-free graphs, this implies bounded clique-width for this class as well. Moreover, known results on unbounded clique-width of certain grids and of split graphs imply that the gem and the co-gem are the only one-vertex P4 extension H such that chordal H-free graphs have bounded clique-width.