, Volume 51, Issue 1, pp 81–98

Treewidth Lower Bounds with Brambles

  • Hans L. Bodlaender
  • Alexander Grigoriev
  • Arie M. C. A. Koster
Open AccessArticle

DOI: 10.1007/s00453-007-9056-z

Cite this article as:
Bodlaender, H.L., Grigoriev, A. & Koster, A.M.C.A. Algorithmica (2008) 51: 81. doi:10.1007/s00453-007-9056-z


In this paper we present a new technique for computing lower bounds for graph treewidth. Our technique is based on the fact that the treewidth of a graph G is the maximum order of a bramble of G minus one. We give two algorithms: one for general graphs, and one for planar graphs. The algorithm for planar graphs is shown to give a lower bound for both the treewidth and branchwidth that is at most a constant factor away from the optimum. For both algorithms, we report on extensive computational experiments that show that the algorithms often give excellent lower bounds, in particular when applied to (close to) planar graphs.


Treewidth Lower bound Bramble Planar graph Grid minor Approximation algorithm 
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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hans L. Bodlaender
    • 1
  • Alexander Grigoriev
    • 2
  • Arie M. C. A. Koster
    • 3
  1. 1.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Quantitative EconomicsUniversity of MaastrichtMaastrichtThe Netherlands
  3. 3.Zuse Institute Berlin (ZIB)Berlin-DahlemGermany