### Abstract

Original language | English |
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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 |
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### Cite this

*Knot Diagrams of Treewidth Two*. Cornell University Library, US: arXiv.org at Cornell University Library. cs.DS

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*Knot Diagrams of Treewidth Two*. cs.DS, vol. 1904.03117v2, arXiv.org at Cornell University Library, Cornell University Library, US.

**Knot Diagrams of Treewidth Two.** / Bodlaender, H.L.; Burton, Benjamin; Fomin, Fedor; Grigoriev, Alexander.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Knot Diagrams of Treewidth Two

AU - Bodlaender, H.L.

AU - Burton, Benjamin

AU - Fomin, Fedor

AU - Grigoriev, Alexander

N1 - data source: NO DATA USED

PY - 2019/4/8

Y1 - 2019/4/8

N2 - 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.

AB - 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.

M3 - Report

VL - 1904.03117v2

T3 - cs.DS

BT - Knot Diagrams of Treewidth Two

PB - arXiv.org at Cornell University Library

CY - Cornell University Library, US

ER -