Knot Diagrams of Treewidth Two
Data Structures and Algorithms
2019-04-09 v2
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 (un)twist and (un)poke Reidemeister moves.
Cite
@article{arxiv.1904.03117,
title = {Knot Diagrams of Treewidth Two},
author = {Hans L. Bodlaender and Benjamin Burton and Fedor V. Fomin and Alexander Grigoriev},
journal= {arXiv preprint arXiv:1904.03117},
year = {2019}
}
Comments
19 pages, 16 figures. The first version had erroneously three subsections repeated; the updated version avoids this mistake