Easy problems for tree-decomposable graphs
Journal of Algorithms
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
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
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
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
Edge dominating set and colorings on graphs with fixed clique-width
Discrete Applied Mathematics
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
Algorithms for vertex-partitioning problems on graphs with fixed clique-width
Theoretical Computer Science
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Clique-width minimization is NP-hard
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
MSOL partitioning problems on graphs of bounded treewidth and clique-width
Theoretical Computer Science
On powers of graphs of bounded NLC-width (clique-width)
Discrete Applied Mathematics
Computing the Tutte Polynomial on Graphs of Bounded Clique-Width
SIAM Journal on Discrete Mathematics
Finding Branch-Decompositions and Rank-Decompositions
SIAM Journal on Computing
Approximating rank-width and clique-width quickly
ACM Transactions on Algorithms (TALG)
Evaluations of Graph Polynomials
Graph-Theoretic Concepts in Computer Science
On the complexity of some colorful problems parameterized by treewidth
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
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We show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are $W[1]$-hard parameterized by clique-width. It was an open problem, explicitly mentioned in several papers, whether any of these problems is fixed parameter tractable when parameterized by the clique-width, that is, solvable in time $g(k)\cdot n^{O(1)}$ on $n$-vertex graphs of clique-width $k$, where $g$ is some function of $k$ only. Our results imply that the running time $O(n^{f(k)})$ of many clique-width-based algorithms is essentially the best we can hope for (up to a widely believed assumption from parameterized complexity, namely $FPT\neq W[1]$).