On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Data reduction for graph coloring problems
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
A basic parameterized complexity primer
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Cluster vertex deletion: a parameterization between vertex cover and clique-width
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Data reduction for graph coloring problems
Information and Computation
Digraph width measures in parameterized algorithmics
Discrete Applied Mathematics
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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 $FPT\neq W[1]$).