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Knot Diagrams of Treewidth Two

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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.
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Original languageEnglish
Place of PublicationCornell University Library, US at Cornell University Library
Number of pages19
Publication statusPublished - 8 Apr 2019

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