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Two Short Proofs Concerning Tree-Decompositions

PATRICK BELLENBAUM, REINHARD DIESTEL

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Source: Crossref

Published: Nov 1, 2002

DOI: 10.1017/s0963548302005369

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Source 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.

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Two Short Proofs Concerning Tree-Decompositions — Mathematical Frontier Network