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New Tools and Simpler Algorithms for Branchwidth

  • Christophe Paul
  • Jan Arne Telle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

We provide new tools, such as k-troikas and good subtree-representations, that allow us to give fast and simple algorithms computing branchwidth. We show that a graph G has branchwidth at most k if and only if it is a subgraph of a chordal graph in which every maximal clique has a k-troika respecting its minimal separators. Moreover, if G itself is chordal with clique tree T then such a chordal supergraph exists having clique tree a minor of T. We use these tools to give a straightforward O(m+n+q 2) algorithm computing branchwidth for an interval graph on m edges, n vertices and q maximal cliques. We also prove a conjecture of F. Mazoit [13] by showing that branchwidth is polynomial on a chordal graph given with a clique tree having a polynomial number of subtrees.

Keywords

Maximal Clique Interval Graph Chordal Graph Minimal Separator Polynomial Number 
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 2005

Authors and Affiliations

  • Christophe Paul
    • 1
  • Jan Arne Telle
    • 2
  1. 1.CNRS – LIRMMMontpellierFrance
  2. 2.Department of InformaticsUniversity of BergenNorway

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