Knot Diagrams of Treewidth Two

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

Research output: Book/ReportReport

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

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