Two Short Proofs Concerning Tree-Decompositions

Authors:
Patrick Bellenbaum;Reinhard Diestel
Affiliations:
Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany (e-mail: diestel@math.uni-hamburg.de);Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, D-20146 Hamburg, Germany (e-mail: diestel@math.uni-hamburg.de)
Venue:
Combinatorics, Probability and Computing
Year:
2002

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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.