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A 4k² kernel for feedback vertex set

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Stéphan ThomasséAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 6, Issue 2

Article No.: 32, Pages 1 - 8

https://doi.org/10.1145/1721837.1721848

Published: 06 April 2010 Publication History

Abstract

We prove that given an undirected graph G on n vertices and an integer k, one can compute, in polynomial time in n, a graph G′ with at most 4k² vertices and an integer k′ such that G has a feedback vertex set of size at most k iff G′ has a feedback vertex set of size at most k′. This result improves a previous O(k¹¹) kernel of Burrage et al., and a more recent cubic kernel of Bodlaender. This problem was communicated by Fellows.

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Cited By

Baumann JPfretzschner MRutter I(2024)Parameterized complexity of vertex splitting to pathwidth at most 1Theoretical Computer Science10.1016/j.tcs.2024.1149281021(114928)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114928
Bai TXiao M(2024)Exact algorithms for restricted subset feedback vertex set in chordal and split graphsTheoretical Computer Science10.1016/j.tcs.2023.114326984(114326)Online publication date: Feb-2024
https://doi.org/10.1016/j.tcs.2023.114326
Donkers HJansen B(2024)Preprocessing to reduce the search spaceJournal of Computer and System Sciences10.1016/j.jcss.2024.103532144:COnline publication date: 18-Jul-2024
https://dl.acm.org/doi/10.1016/j.jcss.2024.103532
Show More Cited By

Index Terms

A 4k² kernel for feedback vertex set
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 6, Issue 2

March 2010

373 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/1721837

Issue’s Table of Contents

Copyright © 2010 ACM.

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Association for Computing Machinery

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Publication History

Published: 06 April 2010

Accepted: 01 May 2009

Revised: 01 April 2009

Received: 01 November 2008

Published in TALG Volume 6, Issue 2

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Cited By

Baumann JPfretzschner MRutter I(2024)Parameterized complexity of vertex splitting to pathwidth at most 1Theoretical Computer Science10.1016/j.tcs.2024.1149281021(114928)Online publication date: Dec-2024
https://doi.org/10.1016/j.tcs.2024.114928
Bai TXiao M(2024)Exact algorithms for restricted subset feedback vertex set in chordal and split graphsTheoretical Computer Science10.1016/j.tcs.2023.114326984(114326)Online publication date: Feb-2024
https://doi.org/10.1016/j.tcs.2023.114326
Donkers HJansen B(2024)Preprocessing to reduce the search spaceJournal of Computer and System Sciences10.1016/j.jcss.2024.103532144:COnline publication date: 18-Jul-2024
https://dl.acm.org/doi/10.1016/j.jcss.2024.103532
Červený RChoudhary PSuchý O(2024)On kernels for d-path vertex coverJournal of Computer and System Sciences10.1016/j.jcss.2024.103531144:COnline publication date: 18-Jul-2024
https://dl.acm.org/doi/10.1016/j.jcss.2024.103531
Dekker DJansen B(2024)Kernelization for feedback vertex set via elimination distance to a forestDiscrete Applied Mathematics10.1016/j.dam.2023.12.016346:C(192-214)Online publication date: 31-Mar-2024
https://dl.acm.org/doi/10.1016/j.dam.2023.12.016
Kammer FSajenko A(2024)Space-Efficient Graph KernelizationsTheory and Applications of Models of Computation10.1007/978-981-97-2340-9_22(260-271)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1007/978-981-97-2340-9_22
Jain PRathore M(2024)Sparsity in Covering SolutionsLATIN 2024: Theoretical Informatics10.1007/978-3-031-55601-2_9(131-146)Online publication date: 6-Mar-2024
https://doi.org/10.1007/978-3-031-55601-2_9
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: 20-Sep-2023
https://doi.org/10.1007/s00224-023-10136-w
Baumann JPfretzschner MRutter I(2023)Parameterized Complexity of Vertex Splitting to Pathwidth at Most 1Graph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_3(30-43)Online publication date: 23-Sep-2023
https://doi.org/10.1007/978-3-031-43380-1_3
Das AKanesh LMadathil JMuluk KPurohit NSaurabh S(2022)On the complexity of singly connected vertex deletionTheoretical Computer Science10.1016/j.tcs.2022.08.012934:C(47-64)Online publication date: 23-Oct-2022
https://dl.acm.org/doi/10.1016/j.tcs.2022.08.012
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