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arXiv · 1904.03117

Knot Diagrams of Treewidth Two

Hans L. Bodlaender·Benjamin Burton·Fedor V. Fomin·Alexander Grigoriev
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Abstract

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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Hans L. Bodlaender, Benjamin Burton, Fedor V. Fomin, Alexander Grigoriev. 2019-04-05. Knot Diagrams of Treewidth Two. https://arxiv.org/abs/1904.03117

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