Turing kernelization for finding long paths and cycles in restricted graph classes
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TLDR
It is proved that k-Path has polynomial-size Turing kernels when restricted to planar graphs, graphs of bounded degree, claw-free graphs, or to K 3 , t -minor-free graph classes.About:
This article is published in Journal of Computer and System Sciences.The article was published on 2017-05-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Chordal graph & Indifference graph.read more
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Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Book
Kernelization: Theory of Parameterized Preprocessing
TL;DR: Kernelization: Theory of Parameterized Preprocessing, by Fomin et al., is unique in that it is a text focusing solely on the titular topic of kernelization, and is able to more effectively showcase and teach the tools used in the field than a more traditional text on fixed parameter complexity.
Book ChapterDOI
Proof of Theorem 1
TL;DR: In this paper, the Neyman-Pearson Lemma was used to prove the existence of intersection points between T and T ∗ in the joint space of W and Z, where each element is a 3D point cloud with k points subsampled from T or T ∆.
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A Polynomial Turing-Kernel for Weighted Independent Set in Bull-Free Graphs
TL;DR: The main result in this paper is to show the existence of an FPT algorithm when the authors parameterize the problem by the solution size k, and it is proved that the chromatic number of a bull-free graph is bounded by a function of its clique number and the maximum chromatics number of its triangle-free induced subgraphs.
Posted Content
Uniform Kernelization Complexity of Hitting Forbidden Minors
TL;DR: It is proved that some Planar F-Minor-Free Deletion problems do not have uniformly polynomial kernels (unless NP ⊆ coNP/poly), not even when parameterized by the vertex cover number.
References
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Book
Graph Theory
TL;DR: Gaph Teory Fourth Edition is standard textbook of modern graph theory which covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each chapter by one or two deeper results.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.
Book
Parameterized complexity theory
Jörg Flum,Martin Grohe +1 more
TL;DR: Fixed-Parameter Tractability.
Book
Parameterized Algorithms
Marek Cygan,Fedor V. Fomin,Lukasz Kowalik,Daniel Lokshtanov,Dániel Marx,Marcin Pilipczuk,Michał Pilipczuk,Saket Saurabh +7 more
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.