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Finite Integer Index of Pathwidth and Treewidth

  • Jakub Gajarský
  • Jan Obdržálek
  • Sebastian OrdyniakEmail author
  • Felix Reidl
  • Peter Rossmanith
  • Fernando Sánchez Villaamil
  • Somnath Sikdar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8894)

Abstract

We show that the optimization versions of the Pathwidth and Treewidth problems have a property called finite integer index when the inputs are restricted to graphs of bounded pathwidth and bounded treewidth, respectively. They do not have this property in general graph classes. This has interesting consequences for kernelization of both these (optimization) problems on certain sparse graph classes. In the process we uncover an interesting property of path and tree decompositions, which might be of independent interest.

Notes

Acknowledgement

We thank Hans L. Bodlaender for valuable discussions about the properties of characteristics of path and tree decompositions.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jakub Gajarský
    • 1
  • Jan Obdržálek
    • 1
  • Sebastian Ordyniak
    • 1
    Email author
  • Felix Reidl
    • 2
  • Peter Rossmanith
    • 2
  • Fernando Sánchez Villaamil
    • 2
  • Somnath Sikdar
    • 2
  1. 1.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic
  2. 2.Theoretical Computer Science, Department of Computer ScienceRWTH Aachen UniversityAachenGermany

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