Two Short Proofs Concerning Tree-Decompositions
PATRICK BELLENBAUM, Reinhard Diestel · Combinatorics Probability Computing · 2002
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.