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 either iterative in nature or not canonical, we give an explicit one-step construction that is canonical.

The key ingredient is an axiomatisation of ‘local properties’ of tangles. Generalisations to locally finite graphs and matroids are also discussed.

中文翻译：

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纠缠

Robertson 和 Seymour 为每个图G构建了一个树分解，可以有效地区分G中的所有缠结。虽然这些分解的所有先前构造本质上都是迭代的或不规范的，但我们给出了一种规范的明确的一步构造。

关键要素是缠结“局部属性”的公理化。还讨论了局部有限图和拟阵的推广。