Well Quasi Orders in Subclasses of Bounded Treewidth Graphs and Their Algorithmic Applications

  • Authors:

  • Michael R. Fellows;Danny Hermelin;Frances A. Rosamond

  • Affiliations:

  • Charles Darwin University, School of Engineering and Information Technology, 0909, Darwin, Northern Territory, Australia;Max Plank Institute for Informatics, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany;Charles Darwin University, School of Engineering and Information Technology, 0909, Darwin, Northern Territory, Australia

  • Venue:
  • Algorithmica - Special Issue: Parameterized and Exact Computation, Part I
  • Year:
  • 2012

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Abstract

We show that three subclasses of bounded treewidth graphs are well quasi ordered by refinements of the minor order. Specifically, we prove that graphs with bounded vertex cover are well quasi ordered by the induced subgraph order, graphs with bounded feedback vertex set are well quasi ordered by the topological-minor order, and graphs with bounded circumference are well quasi ordered by the induced minor order. Our results give algorithms for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.