### 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.

Original language | English |
---|---|

Place of Publication | Cornell University Library, US |

Publisher | arXiv.org at Cornell University Library |

Number of pages | 19 |

Volume | 1904.03117v2 |

Publication status | Published - 8 Apr 2019 |

### Publication series

Series | cs.DS |
---|

### JEL classifications

- c00 - Mathematical and Quantitative Methods: General

## Cite this

Bodlaender, H. L., Burton, B., Fomin, F., & Grigoriev, A. (2019).

*Knot Diagrams of Treewidth Two*. arXiv.org at Cornell University Library. cs.DS https://arxiv.org/abs/1904.03117