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Generation of Graphs with Bounded Branchwidth

  • Christophe Paul
  • Andrzej Proskurowski
  • Jan Arne Telle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4271)

Abstract

Branchwidth is a connectivity parameter of graphs closely related to treewidth. Graphs of treewidth at most k can be generated algorithmically as the subgraphs of k-trees. n this paper, we investigate the family of edge-maximal graphs of branchwidth k, that we call k-branches. The k-branches are, just as the k-trees, a subclass of the chordal graphs where all minimal separators have size k. However, a striking difference arises when considering subgraph-minimal members of the family. Whereas K k + 1 is the only subgraph-minimal k-tree, we show that for any k ≥7 a minimal k-branch having q maximal cliques exists for any value of \(q \not\in \{3,5\}\), except for k=8,q=2. We characterize subgraph-minimal k-branches for all values of k. Our investigation leads to a generation algorithm, that adds one or two new maximal cliques in each step, producing exactly the k-branches.

Keywords

Planar Graph Maximal Clique Chordal Graph Minimal Separator Mathematical Society Lecture Note Series 
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 2006

Authors and Affiliations

  • Christophe Paul
    • 1
  • Andrzej Proskurowski
    • 2
  • Jan Arne Telle
    • 3
  1. 1.CNRS – LIRMMMontpellierFrance
  2. 2.Department of Computer and Information ScienceUniversity of OregonUSA
  3. 3.Department of InformaticsUniversity of BergenNorway

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