Large-treewidth graph decompositions and applications

  • Authors:

  • Chandra Chekuri;Julia Chuzhoy

  • Affiliations:

  • University of Illinois, Urbana, IL, USA;Toyota Technological Institute, Chicago, IL, USA

  • Venue:
  • Proceedings of the forty-fifth annual ACM symposium on Theory of computing
  • Year:
  • 2013

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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.