A special planar satisfiability problem and a consequence of its NP-completeness
Discrete Applied Mathematics
Motif Search in Graphs: Application to Metabolic Networks
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Graph Layout Problems Parameterized by Vertex Cover
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
SIAM Journal on Discrete Mathematics
What Makes Equitable Connected Partition Easy
Parameterized and Exact Computation
On parse trees and Myhill-Nerode-type tools for handling graphs of bounded rank-width
Discrete Applied Mathematics
Improved upper bounds for vertex cover
Theoretical Computer Science
Algorithmic meta-theorems for restrictions of treewidth
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
On the complexity of some colorful problems parameterized by treewidth
Information and Computation
Upper and lower bounds for finding connected motifs in vertex-colored graphs
Journal of Computer and System Sciences
Parameterized complexity of coloring problems: Treewidth versus vertex cover
Theoretical Computer Science
Thread Graphs, Linear Rank-Width and Their Algorithmic Applications
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Parameterized Complexity
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
When trees grow low: shrubs and fast MSO1
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
European Journal of Combinatorics
Preprocessing subgraph and minor problems: when does a small vertex cover help?
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Model checking lower bounds for simple graphs
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
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Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. In this context, vertex cover is used as a powerful parameter for dealing with problems which are hard to solve even on graphs of bounded tree-width. The drawback of vertex cover is that bounding it severely restricts admissible graph classes. We introduce a new parameter called twin-cover and show that it is capable of solving a wide range of hard problems while also being much less restrictive than vertex cover and attaining low values even on dense graphs. The article begins by introducing a new FPT algorithm for Graph Motif on graphs of bounded vertex cover. This is the first algorithm of this kind for Graph Motif. We continue by defining twin-cover and providing some related results and notions. The next section contains a number of new FPT algorithms on graphs of bounded twin-cover, with a special emphasis on solving problems which are hard even on graphs of bounded tree-width. Finally, section five generalizes the recent results of Michael Lampis for MS1 model checking from vertex cover to twin-cover.