Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Min cut is NP-complete for edge weighted trees
Theoretical Computer Science - Thirteenth International Colloquim on Automata, Languages and Programming, Renne
The pathwidth and treewidth of cographs
SIAM Journal on Discrete Mathematics
On the pathwidth of chordal graphs
Discrete Applied Mathematics - ARIDAM IV and V
The vertex separation and search number of a graph
Information and Computation
Triangulating graphs without asteroidal triples
Discrete Applied Mathematics
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Safe Reduction Rules for Weighted Treewidth
Algorithmica
Invitation to data reduction and problem kernelization
ACM SIGACT News
On problems without polynomial kernels
Journal of Computer and System Sciences
New lower and upper bounds for graph treewidth
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
Preprocessing for treewidth: a combinatorial analysis through kernelization
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
TREEWIDTH and PATHWIDTH parameterized by the vertex cover number
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Preprocessing subgraph and minor problems: When does a small vertex cover help?
Journal of Computer and System Sciences
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Assuming the AND-distillation conjecture, the Pathwidth problem of determining whether a given graph G has pathwidth at most k admits no polynomial kernelization with respect to k. The present work studies the existence of polynomial kernels for Pathwidth with respect to other, structural, parameters. Our main result is that, unless NP ⊆ coNP/poly, Pathwidth admits no polynomial kernelization even when parameterized by the vertex deletion distance to a clique, by giving a cross-composition from Cutwidth. The cross-composition works also for Treewidth, improving over previous lower bounds by the present authors. For Pathwidth, our result rules out polynomial kernels with respect to the distance to various classes of polynomial-time solvable inputs, like interval or cluster graphs. This leads to the question whether there are nontrivial structural parameters for which Pathwidth does admit a polynomial kernelization. To answer this, we give a collection of graph reduction rules that are safe for Pathwidth. We analyze the success of these results and obtain polynomial kernelizations with respect to the following parameters: the size of a vertex cover of the graph, the vertex deletion distance to a graph where each connected component is a star, and the vertex deletion distance to a graph where each connected component has at most c vertices.