article

Preprocessing subgraph and minor problems: When does a small vertex cover help?

Authors:

Fedor V. Fomin,

Bart M. P. Jansen,

Michał PilipczukAuthors Info & Claims

Journal of Computer and System Sciences, Volume 80, Issue 2

Pages 468 - 495

https://doi.org/10.1016/j.jcss.2013.09.004

Published: 01 March 2014 Publication History

Abstract

We prove a number of results around kernelization of problems parameterized by the size of a given vertex cover of the input graph. We provide three sets of simple general conditions characterizing problems admitting kernels of polynomial size. Our characterizations not only give generic explanations for the existence of many known polynomial kernels for problems like q-Coloring, Odd Cycle Transversal, Chordal Deletion, @h-Transversal, or Long Path, parameterized by the size of a vertex cover, but also imply new polynomial kernels for problems like F-Minor-Free Deletion, which is to delete at most k vertices to obtain a graph with no minor from a fixed finite set F. While our characterization captures many interesting problems, the kernelization complexity landscape of parameterizations by vertex cover is much more involved. We demonstrate this by several results about induced subgraph and minor containment testing.

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Cited By

Agrawal ALokshtanov DMisra PSaurabh SZehavi M(2023)Polynomial Kernel for Interval Vertex DeletionACM Transactions on Algorithms10.1145/357107519:2(1-68)Online publication date: 15-Apr-2023
https://dl.acm.org/doi/10.1145/3571075
Oostveen Jvan Leeuwen E(2023)Streaming deletion problems parameterized by vertex coverTheoretical Computer Science10.1016/j.tcs.2023.114178979:COnline publication date: 10-Nov-2023
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Bishnu AGhosh AKolay SMishra GSaurabh S(2023)Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data StreamsTheory of Computing Systems10.1007/s00224-023-10136-w67:6(1241-1267)Online publication date: 1-Dec-2023
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Preprocessing subgraph and minor problems: When does a small vertex cover help?
1. Mathematics of computing
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    1. Graph theory
2. Theory of computation

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cover image Journal of Computer and System Sciences

Journal of Computer and System Sciences Volume 80, Issue 2

March, 2014

178 pages

ISSN:0022-0000

Issue’s Table of Contents

Copyright © Elsevier Inc. © 2013.

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Academic Press, Inc.

United States

Publication History

Published: 01 March 2014

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Cited By

Agrawal ALokshtanov DMisra PSaurabh SZehavi M(2023)Polynomial Kernel for Interval Vertex DeletionACM Transactions on Algorithms10.1145/357107519:2(1-68)Online publication date: 15-Apr-2023
https://dl.acm.org/doi/10.1145/3571075
Oostveen Jvan Leeuwen E(2023)Streaming deletion problems parameterized by vertex coverTheoretical Computer Science10.1016/j.tcs.2023.114178979:COnline publication date: 10-Nov-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.114178
Bishnu AGhosh AKolay SMishra GSaurabh S(2023)Small Vertex Cover Helps in Fixed-Parameter Tractability of Graph Deletion Problems over Data StreamsTheory of Computing Systems10.1007/s00224-023-10136-w67:6(1241-1267)Online publication date: 1-Dec-2023
https://dl.acm.org/doi/10.1007/s00224-023-10136-w
Jansen Bde Kroon J(2022)Preprocessing vertex-deletion problemsJournal of Computer and System Sciences10.1016/j.jcss.2021.12.003126:C(59-79)Online publication date: 1-Jun-2022
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Oostveen Jvan Leeuwen E(2021)Streaming Deletion Problems Parameterized by Vertex CoverFundamentals of Computation Theory10.1007/978-3-030-86593-1_29(413-426)Online publication date: 12-Sep-2021
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Bishnu AGhosh AKolay SMishra GSaurabh S(2020)Fixed Parameter Tractability of Graph Deletion Problems over Data StreamsComputing and Combinatorics10.1007/978-3-030-58150-3_53(652-663)Online publication date: 29-Aug-2020
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Agrawal AMisra PSaurabh SZehavi MChan T(2019)Interval vertex deletion admits a polynomial kernelProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3310435.3310538(1711-1730)Online publication date: 6-Jan-2019
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Donkers HJansen B(2019)A Turing Kernelization Dichotomy for Structural Parameterizations of -Minor-Free DeletionGraph-Theoretic Concepts in Computer Science10.1007/978-3-030-30786-8_9(106-119)Online publication date: 19-Jun-2019
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Jansen BPilipczuk MKlein P(2017)Approximation and kernelization for chordal vertex deletionProceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3039686.3039777(1399-1418)Online publication date: 16-Jan-2017
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