Constructing Brambles

  • Mathieu Chapelle
  • Frédéric Mazoit
  • Ioan Todinca
Conference paper

DOI: 10.1007/978-3-642-03816-7_20

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5734)
Cite this paper as:
Chapelle M., Mazoit F., Todinca I. (2009) Constructing Brambles. In: Královič R., Niwiński D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg

Abstract

Given an arbitrary graph G and a number k, it is well-known by a result of Seymour and Thomas [22] that G has treewidth strictly larger than k if and only if it has a bramble of order k + 2. Brambles are used in combinatorics as certificates proving that the treewidth of a graph is large. From an algorithmic point of view there are several algorithms computing tree-decompositions of G of width at most k, if such decompositions exist and the running time is polynomial for constant k. Nevertheless, when the treewidth of the input graph is larger than k, to our knowledge there is no algorithm constructing a bramble of order k + 2. We give here such an algorithm, running in \({\mathcal O}(n^{k+4})\) time. For classes of graphs with polynomial number of minimal separators, we define a notion of compact brambles and show how to compute compact brambles of order k + 2 in polynomial time, not depending on k.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mathieu Chapelle
    • 1
  • Frédéric Mazoit
    • 2
  • Ioan Todinca
    • 1
  1. 1.LIFOUniversité d’OrléansOrléans Cedex 2France
  2. 2.LaBRIUniversité de BordeauxTalence CedexFrance

Personalised recommendations