The monadic second-order logic of graphs. I. recognizable sets of finite graphs
Information and Computation
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Parallel Algorithms for Series Parallel Graphs
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Graph Minors. XX. Wagner's conjecture
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Theory of Computing Systems
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
Cutset sampling for Bayesian networks
Journal of Artificial Intelligence Research
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Hitting and harvesting pumpkins
ESA'11 Proceedings of the 19th European conference on Algorithms
Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
On feedback vertex set new measure and new structures
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Finding odd cycle transversals
Operations Research Letters
A single-exponential FPT algorithm for the K4- minor cover problem
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Parameterized Complexity
A single-exponential FPT algorithm for the K4- minor cover problem
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Linear kernels and single-exponential algorithms via protrusion decompositions
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Given an input graph G on n vertices and an integer k, the parameterized K4-minor cover problem asks whether there is a set S of at most k vertices whose deletion results in a K4-minor free graph or, equivalently, in a graph of treewidth at most 2. The problem can thus also be called Treewidth-2 Vertex Deletion. This problem is inspired by two well-studied parameterized vertex deletion problems, Vertex Cover and Feedback Vertex Set, which can be expressed as Treewidth-tVertex Deletion problems: t=0 for Vertex Cover and t=1 for Feedback Vertex Set. While a single-exponential FPT algorithm has been known for a long time for Vertex Cover, such an algorithm for Feedback Vertex Set was devised comparatively recently. While it is known to be unlikely that Treewidth-tVertex Deletion can be solved in time co(k)·nO(1), it was open whether the K4-minor cover could be solved in single-exponential FPT time, i.e. in ck·nO(1) time. This paper answers this question in the affirmative.