Knot Diagrams of Treewidth Two

Hans L. Bodlaender*, Benjamin Burton, Fedor V. Fomin, Alexander Grigoriev

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic


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 trivial knot? 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 trivial knot of treewidth 2 can always be reduced to the trivial diagram with at most n untwist and unpoke Reidemeister moves.
Original languageEnglish
Title of host publicationGraph-Theoretic Concepts in Computer Science
Subtitle of host publication46th International Workshop, WG 2020, Leeds, UK, June 24–26, 2020, Revised Selected Papers
EditorsIsolde Adler, Haiko Müller
Place of PublicationCham
PublisherSpringer Nature Switzerland AG
Number of pages12
ISBN (Electronic)978-3-030-60440-0
ISBN (Print)978-3-030-60439-4
Publication statusPublished - 9 Oct 2020
EventInternational Workshop on Graph-Theoretic Concepts in Computer Science - Leeds, United Kingdom
Duration: 24 Jun 202026 Jun 2020
Conference number: 46

Publication series

SeriesLecture Notes in Computer Science


WorkshopInternational Workshop on Graph-Theoretic Concepts in Computer Science
Abbreviated titleWG 2020
Country/TerritoryUnited Kingdom
Internet address

JEL classifications

  • c02 - Mathematical Methods


  • Knot diagrams
  • Knot theory
  • Graph algorithms
  • Treewidth
  • Series parallel graphs

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