Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
k-NLC graphs and polynomial algorithms
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
How to Solve NP-hard Graph Problems on Clique-Width Bounded Graphs in Polynomial Time
WG '01 Proceedings of the 27th International Workshop on Graph-Theoretic Concepts in Computer Science
Chordal co-gem-free and (P5,gem)-freegraphs have bounded clique-width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Vertex disjoint paths on clique-width bounded graphs
Theoretical Computer Science
The relative clique-width of a graph
Journal of Combinatorial Theory Series B
Chordal co-gem-free and (P5,gem)-free graphs have bounded clique-width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
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Treewidth is generally regarded as one of the most useful parameterizations of a graph's construction. Clique-width is a similar parameterizations that shares one of the powerful properties of treewidth, namely: if a graph is of bounded treewidth (or clique-width), then there is a polynomial time algorithm for any graph problem expressible in Monadic Second Order Logic, using quantifiers on vertices (in the case of clique-width you must assume a clique-width parse expression is given). In studying the relationship between treewidth and clique-width, Courcelle and Olariu showed that any graph of bounded treewidth is also of bounded clique-width; in particular, for any graph G with treewidth k, the clique-width of G 驴 4 * 2k-1 + 1.In this paper, we improve this result to the clique-width of G 驴 3 * 2k-1 and more importantly show that there is an exponential lower bound on this relationship. In particular, for any k, there is a graph G with treewidth = k where the clique-width of G 驴 2驴k/2驴-1.