Robertson and Seymour constructed for every graph $G$ a tree-decomposition that efficiently distinguishes all the tangles in $G$. While all previous constructions of these decompositions are iterative in nature, we give an explicit one-step construction. The key ingredient is an axiomatisation of 'local properties' of tangles. Generalisations to locally finite graphs and matroids are also discussed.

翻译：Robertson和Seymour为每张图都建造了G$的树分解装置,它有效地区分了以G$计算的所有三角形。虽然以前所有这些分解装置都是迭接的,但我们给出了一个明确的一步构造。关键成分是三角形的“本地属性”的对齐化。 也讨论了对本地定数图和类固醇的概括化。