Knot Diagrams of Treewidth Two

H.L. Bodlaender, Benjamin Burton, Fedor Fomin, Alexander Grigoriev

Research output: Book/ReportReportAcademic


In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most n (un)twist and (un)poke Reidemeister moves.
Original languageEnglish
Place of PublicationCornell University Library, US
PublisherCornell University - arXiv
Number of pages19
Publication statusPublished - 8 Apr 2019

Publication series


JEL classifications

  • c00 - Mathematical and Quantitative Methods: General


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