Knot Diagrams of Treewidth Two

H.L. Bodlaender, Benjamin Burton, Fedor Fomin, Alexander Grigoriev

Research output: Book/ReportReportAcademic

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 languageEnglish
Place of PublicationCornell University Library, US
PublisherarXiv.org at Cornell University Library
Number of pages19
Volume1904.03117v2
Publication statusPublished - 8 Apr 2019

Publication series

Seriescs.DS

Cite this

Bodlaender, H. L., Burton, B., Fomin, F., & Grigoriev, A. (2019). Knot Diagrams of Treewidth Two. Cornell University Library, US: arXiv.org at Cornell University Library. cs.DS
Bodlaender, H.L. ; Burton, Benjamin ; Fomin, Fedor ; Grigoriev, Alexander. / Knot Diagrams of Treewidth Two. Cornell University Library, US : arXiv.org at Cornell University Library, 2019. 19 p. (cs.DS).
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Bodlaender, HL, Burton, B, Fomin, F & Grigoriev, A 2019, 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.

Cornell University Library, US : arXiv.org at Cornell University Library, 2019. 19 p. (cs.DS).

Research output: Book/ReportReportAcademic

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

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T3 - cs.DS

BT - Knot Diagrams of Treewidth Two

PB - arXiv.org at Cornell University Library

CY - Cornell University Library, US

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Bodlaender HL, Burton B, Fomin F, Grigoriev A. Knot Diagrams of Treewidth Two. Cornell University Library, US: arXiv.org at Cornell University Library, 2019. 19 p. (cs.DS).