The maximum k-colorable subgraph problem for chordal graphs
Information Processing Letters
The complexity of generalized clique covering
Discrete Applied Mathematics
The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
COCO '99 Proceedings of the Fourteenth Annual IEEE Conference on Computational Complexity
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques
Theory of Computing Systems
Almost 2-SAT Is Fixed-Parameter Tractable (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
Finding a maximum-weight induced k-partite subgraph of an i-triangulated graph
Discrete Applied Mathematics
The complexity of finding subgraphs whose matching number equals the vertex cover number
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
Vertex Cover Problem Parameterized Above and Below Tight Bounds
Theory of Computing Systems
Paths, flowers and vertex cover
ESA'11 Proceedings of the 19th European conference on Algorithms
On multiway cut parameterized above lower bounds
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
On polynomial kernels for structural parameterizations of odd cycle transversal
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
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Vertex cover and odd cycle transversal are minimum cardinality sets of vertices of a graph whose deletion makes the resultant graph 1-colorable and 2-colorable, respectively. As a natural generalization of these well-studied problems, we consider the Graph r-Partization problem of finding a minimum cardinality set of vertices whose deletion makes the graph r-colorable. We explore further connections to Vertex Cover by introducing Generalized Above Guarantee Vertex Cover, a variant of Vertex Cover defined as: Given a graph G, a clique cover $\cal K$ of G and a non-negative integer k, does G have a vertex cover of size at most $k+\sum_{C \in \cal K}(|C|-1)$? We study the parameterized complexity hardness of this problem by a reduction from r-Partization. We then describe sequacious fixed-parameter tractability results for r-Partization, parameterized by the solution size k and the required chromaticity r, in perfect graphs and split graphs. For Odd Cycle Transversal, we describe an O*(2k) algorithm for perfect graphs and a polynomial-time algorithm for co-chordal graphs.