research-article

Large-treewidth graph decompositions and applications

Authors:

Chandra Chekuri,

Julia ChuzhoyAuthors Info & Claims

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

Pages 291 - 300

https://doi.org/10.1145/2488608.2488645

Published: 01 June 2013 Publication History

Abstract

Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph G into node-disjoint subgraphs, where each subgraph has sufficiently large treewidth. We prove two theorems on the tradeoff between the number of the desired subgraphs h, and the desired lower bound r on the treewidth of each subgraph. The theorems assert that, given a graph G with treewidth k, a decomposition with parameters h,r is feasible whenever hr² ≤ k/polylog(k), or h³r ≤ k/polylog(k) holds. We then show a framework for using these theorems to bypass the well-known Grid-Minor Theorem of Robertson and Seymour in some applications. In particular, this leads to substantially improved parameters in some Erdos-Posa-type results, and faster algorithms for some fixed-parameter tractable problems.

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Index Terms

Large-treewidth graph decompositions and applications
1. Theory of computation
  1. Randomness, geometry and discrete structures

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cover image ACM Conferences

STOC '13: Proceedings of the forty-fifth annual ACM symposium on Theory of Computing

June 2013

998 pages

ISBN:9781450320290

DOI:10.1145/2488608

General Chairs:
Dan Boneh
Stanford University, USA
,
Tim Roughgarden
Stanford University, USA
,
Program Chair:
Joan Feigenbaum
Yale University, USA

Copyright © 2013 ACM.

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Published: 01 June 2013

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STOC'13: Symposium on Theory of Computing

June 1 - 4, 2013

California, Palo Alto, USA

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STOC '13 Paper Acceptance Rate 100 of 360 submissions, 28%;

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

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https://doi.org/10.1007/s00493-021-4743-y
Agrawal ALokshtanov DMisra PSaurabh SZehavi M(2022)Erdős–Pósa property of obstructions to interval graphsJournal of Graph Theory10.1002/jgt.22895102:4(702-727)Online publication date: 29-Sep-2022
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Masařík TPilipczuk MRzążewski PSorge M(2021)Constant Congestion Brambles in Directed GraphsExtended Abstracts EuroComb 202110.1007/978-3-030-83823-2_50(318-324)Online publication date: 24-Aug-2021
https://doi.org/10.1007/978-3-030-83823-2_50
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