On the tree-width of knot diagrams

Arnaud de Mesmay, Jessica Purcell, Saul Schleimer, Eric Sedgwick

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4 Citations (Scopus)


We show that a small tree-decomposition of a knot diagram induces a small sphere-decomposition of the corresponding knot. This, in turn, implies that the knot admits a small essential planar meridional surface or a small bridge sphere. We use this to give the first examples of knots where any diagram has high tree-width. This answers a question of Burton and of Makowsky and Mariño.

Original languageEnglish
Pages (from-to)164-180
Number of pages17
JournalJournal of Computational Geometry
Issue number1
Publication statusPublished - 1 Jan 2019

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