Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-30T07:06:11.302Z Has data issue: false hasContentIssue false
  • English
  • Français

Two Short Proofs Concerning Tree-Decompositions

Published online by Cambridge University Press:  21 November 2002

PATRICK BELLENBAUM  and
REINHARD DIESTEL
PATRICK BELLENBAUM
Affiliation:
Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany (e-mail: diestel@math.uni-hamburg.de)
REINHARD DIESTEL
Affiliation:
Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany (e-mail: diestel@math.uni-hamburg.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 6 , November 2002 , pp. 541 - 547
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)