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On the tree-width of knot diagrams
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Schleimer, Saul, de Mesmay, Arnaud, Purcell, Jessica and Sedgwick, Eric (2019) On the tree-width of knot diagrams. Journal of Computational Geometry, 10 (1). pp. 164-180. ISSN 1920-180X.
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Official URL: https://jocg.org/index.php/jocg/article/view/3072/...
Abstract
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.
| Item Type: | Journal Article | ||||||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
| Library of Congress Subject Headings (LCSH): | Graph theory, Knot theory | ||||||||||||
| Journal or Publication Title: | Journal of Computational Geometry | ||||||||||||
| Publisher: | Carleton University ; Computational Geometry Laboratory | ||||||||||||
| ISSN: | 1920-180X | ||||||||||||
| Official Date: | 27 May 2019 | ||||||||||||
| Dates: |
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| Volume: | 10 | ||||||||||||
| Number: | 1 | ||||||||||||
| Page Range: | pp. 164-180 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | Published | ||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||
| Date of first compliant deposit: | 21 May 2019 | ||||||||||||
| Date of first compliant Open Access: | 22 May 2019 | ||||||||||||
| RIOXX Funder/Project Grant: |
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