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.
|Place of Publication||Cornell University Library, US|
|Publisher||arXiv.org at Cornell University Library|
|Number of pages||19|
|Publication status||Published - 8 Apr 2019|
- c00 - Mathematical and Quantitative Methods: General