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Finding topological subgraphs is fixed-parameter tractable

Authors:

Ken-ichi Kawarabayashi,

Paul WollanAuthors Info & Claims

STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computing

Pages 479 - 488

https://doi.org/10.1145/1993636.1993700

Published: 06 June 2011 Publication History

Abstract

We prove that for every fixed undirected graph H, there is an O(|V(G)|³) time algorithm that, given a graph G, tests if G contains H as a topological subgraph (that is, a subdivision of H is subgraph of G). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every H we obtain an O(|V(G)|³) time algorithm that tests if there is an immersion of H into a given graph G. This answers another open question raised by Downey and Fellows in 1992.

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Cited By

Schirrmacher NSiebertz SStamoulis GThilikos DVigny ASobocinski PLago UEsparza J(2024)Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph ClassesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662089(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662089
Sau IStamoulis GThilikos D(2024)A more accurate view of the Flat Wall TheoremJournal of Graph Theory10.1002/jgt.23121107:2(263-297)Online publication date: 13-May-2024
https://doi.org/10.1002/jgt.23121
Golovach PStamoulis GThilikos D(2023)Hitting Topological Minor Models in Planar Graphs is Fixed Parameter TractableACM Transactions on Algorithms10.1145/358368819:3(1-29)Online publication date: 10-Feb-2023
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Index Terms

Finding topological subgraphs is fixed-parameter tractable
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '11: Proceedings of the forty-third annual ACM symposium on Theory of computing

June 2011

840 pages

ISBN:9781450306911

DOI:10.1145/1993636

General Chair:
Lance Fortnow
Northwestern University
,
Program Chair:
Salil Vadhan
Harvard University

Copyright © 2011 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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New York, NY, United States

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Published: 06 June 2011

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STOC'11: Symposium on Theory of Computing

June 6 - 8, 2011

California, San Jose, USA

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STOC '11 Paper Acceptance Rate 84 of 304 submissions, 28%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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https://dl.acm.org/doi/10.1145/3661814.3662089
Sau IStamoulis GThilikos D(2024)A more accurate view of the Flat Wall TheoremJournal of Graph Theory10.1002/jgt.23121107:2(263-297)Online publication date: 13-May-2024
https://doi.org/10.1002/jgt.23121
Golovach PStamoulis GThilikos D(2023)Hitting Topological Minor Models in Planar Graphs is Fixed Parameter TractableACM Transactions on Algorithms10.1145/358368819:3(1-29)Online publication date: 10-Feb-2023
https://dl.acm.org/doi/10.1145/3583688
Fomin FGolovach PStamoulis GThilikos D(2023)An Algorithmic Meta-Theorem for Graph Modification to Planarity and FOLACM Transactions on Computation Theory10.1145/357127814:3-4(1-29)Online publication date: 1-Feb-2023
https://dl.acm.org/doi/10.1145/3571278
Włodarczyk MZehavi M(2023)Planar Disjoint Paths, Treewidth, and Kernels2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00044(649-662)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00044
Ibiapina ASilva A(2023)Mengerian graphs: characterization and recognitionJournal of Computer and System Sciences10.1016/j.jcss.2023.103467(103467)Online publication date: Aug-2023
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Ganian RKim ESzeider S(2022)Algorithmic Applications of Tree-Cut WidthSIAM Journal on Discrete Mathematics10.1137/20M137478X36:4(2635-2666)Online publication date: 1-Jan-2022
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Golovach PPanolan FRai ASaurabh S(2022)Parameterized Complexity of Set-Restricted Disjoint Paths on Chordal GraphsComputer Science – Theory and Applications10.1007/978-3-031-09574-0_10(152-169)Online publication date: 24-Jun-2022
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Fomin FLokshtanov DMihajlin ISaurabh SZehavi M(2021)Computation of Hadwiger Number and Related Contraction ProblemsACM Transactions on Computation Theory10.1145/344863913:2(1-25)Online publication date: 26-Mar-2021
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Golovach PPaulusma Dvan Leeuwen E(2021)Induced Disjoint Paths in AT-free GraphsJournal of Computer and System Sciences10.1016/j.jcss.2021.10.003Online publication date: Oct-2021
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