Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
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
On the Relationship Between Clique-Width and Treewidth
SIAM Journal on Computing
On the complexity of fixed parameter problems
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Clique-width: on the price of generality
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Parameterized Complexity of Coloring Problems: Treewidth versus Vertex Cover
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
SIAM Journal on Discrete Mathematics
Iterative compression and exact algorithms
Theoretical Computer Science
Fixed-Parameter Algorithms for Cluster Vertex Deletion
Theory of Computing Systems - Special Section: Algorithmic Game Theory; Guest Editors: Burkhard Monien and Ulf-Peter Schroeder
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Twin-Cover: beyond vertex cover in parameterized algorithmics
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized Complexity
Constant thresholds can make target set selection tractable
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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The cluster vertex deletion number of a graph is the minimum number of its vertices whose deletion results in a disjoint union of complete graphs. This generalizes the vertex cover number, provides an upper bound to the clique-width and is related to the previously studied notion of the twin cover of the graph under consideration. We study the fixed parameter tractability of basic graph theoretic problems related to coloring and Hamiltonicity parameterized by cluster vertex deletion number. Our results show that most of these problems remain fixed parameter tractable as well, and thus we push the borderline between tractability and intractability towards the clique-width parameter.