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 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 language | English |
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Title of host publication | Graph-Theoretic Concepts in Computer Science |
Subtitle of host publication | 46th International Workshop, WG 2020, Leeds, UK, June 24–26, 2020, Revised Selected Papers |
Editors | Isolde Adler, Haiko Müller |
Place of Publication | Cham |
Publisher | Springer Nature Switzerland AG |
Pages | 80-91 |
Number of pages | 12 |
ISBN (Electronic) | 978-3-030-60440-0 |
ISBN (Print) | 978-3-030-60439-4 |
DOIs | |
Publication status | Published - 9 Oct 2020 |
Event | International Workshop on Graph-Theoretic Concepts in Computer Science - Leeds, United Kingdom Duration: 24 Jun 2020 → 26 Jun 2020 Conference number: 46 https://algorithms.leeds.ac.uk/wg2020/ |
Publication series
Series | Lecture Notes in Computer Science |
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Volume | 12301 |
ISSN | 0302-9743 |
Workshop
Workshop | International Workshop on Graph-Theoretic Concepts in Computer Science |
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Abbreviated title | WG 2020 |
Country/Territory | United Kingdom |
City | Leeds |
Period | 24/06/20 → 26/06/20 |
Internet address |
JEL classifications
- c02 - Mathematical Methods
Keywords
- Knot diagrams
- Knot theory
- Graph algorithms
- Treewidth
- Series parallel graphs