On search decision and the efficiency of polynomial-time algorithms
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Obstruction set isolation for the gate matrix layout problem
Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Monadic Second Order Logic, Tree Automata and Forbidden Minors
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Graph bandwidth of weighted caterpillars
Theoretical Computer Science - Algorithmic applications in management
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Invitation to data reduction and problem kernelization
ACM SIGACT News
An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Theory of Computing Systems
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
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 cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Treewidth: characterizations, applications, and computations
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
On feedback vertex set new measure and new structures
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
The undirected feedback vertex set problem has a poly(k) kernel
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Survey: Subexponential parameterized algorithms
Computer Science Review
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
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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The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP-complete. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G = (V, E), k); |V| = n, we can construct, in polynomial time, an instance (G′, k′) such that (i) (G, k) is a YES instance if and only if (G′, k′) is a YES instance, (ii) G′ has O(k4) vertices, and (iii) k′ ≤ k. We also give a fixed parameter tractable (FPT) algorithm for the problem that runs in O(7kk ċ n2) time.