Fixed-parameter tractability of graph modification problems for hereditary properties
Information Processing Letters
Graph classes: a survey
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Invitation to data reduction and problem kernelization
ACM SIGACT News
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A Problem Kernelization for Graph Packing
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
Algorithmics of Large and Complex Networks
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
A Cubic Kernel for Feedback Vertex Set and Loop Cutset
Theory of Computing Systems - Special Issue: Theoretical Aspects of Computer Science; Guest Editors: Wolgang Thomas and Pascal Weil
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Chordal Deletion is Fixed-Parameter Tractable
Algorithmica
Obtaining a planar graph by vertex deletion
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Wheel-free deletion is W[2]-hard
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A kernelization algorithm for d-Hitting Set
Journal of Computer and System Sciences
Improved upper bounds for vertex cover
Theoretical Computer Science
Isomorphism for graphs of bounded feedback vertex set number
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
Faster parameterized algorithms for deletion to split graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
European Journal of Combinatorics
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Split Vertex Deletion meets Vertex Cover: New fixed-parameter and exact exponential-time algorithms
Information Processing Letters
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Vertex deletion problems are at the heart of parameterized complexity. For a graph class F, the F-Deletion problem takes as input a graph G and an integer k. The question is whether it is possible to delete at most k vertices from G such that the resulting graph belongs to F. Whether Perfect Deletion is fixed-parameter tractable, and whether Chordal Deletion admits a polynomial kernel, when parameterized by k, have been stated as open questions in previous work. We show that Perfect Deletion (k) and Weakly Chordal Deletion (k) are W[2]-hard. In search of positive results, we study restricted variants such that the deleted vertices must be taken from a specified set X, which we parameterize by |X|. We show that for Perfect Deletion and Weakly Chordal Deletion, although this restriction immediately ensures fixed parameter tractability, it is not enough to yield polynomial kernels, unless NP ⊆ coNP/poly. On the positive side, for Chordal Deletion, the restriction enables us to obtain a kernel with O(|X|4) vertices.