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Dominating Sets and Local Treewidth

  • Fedor V. Fomin
  • Dimtirios M. Thilikos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2832)

Abstract

It is known that the treewidth of a planar graph with a dominating set of size d is \(O(\sqrt{d})\) and this fact is used as the basis for several fixed parameter algorithms on planar graphs. An interesting question motivating our study is if similar bounds can be obtained for larger minor closed graph families. We say that a graph family \(\mathcal{F}\) has the domination-treewidth property if there is some function f(d) such that every graph \(G \in \mathcal{F}\) with dominating set of size ≤ d has treewidth ≤ f(d). We show that a minor-closed graph family \(\mathcal{F}\) has the domination-treewidth property if and only if \(\mathcal{F}\) has bounded local treewidth. This result has important algorithmic consequences.

Keywords

Planar Graph Tree Decomposition Graph Class Subgraph Isomorphism Graph Family 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Dimtirios M. Thilikos
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Departament de Llenguatges i Sistemes InformàticsUniversitat Politècnica de CatalunyaBarcelonaSpain

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