Entanglements

05/23/2022

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by   Johannes Carmesin, et al.

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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.