Stick numbers of 2-bridge knots and links

Youngsik Huh, Sungjong No, Seung Sang Oh

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of the minimal crossing number c(K) of the knot, which is s(K) ≤ 2c(K). Furthermore, McCabe proved that s(K) ≤ c(K) + 3 for a 2-bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any 2-bridge knot or link K of at least six crossings by using only c(K)+2 straight sticks. This gives a new upper bound on stick numbers of 2-bridge knots and links in terms of crossing numbers.

Original languageEnglish
Pages (from-to)4143-4152
Number of pages10
JournalProceedings of the American Mathematical Society
Volume139
Issue number11
DOIs
Publication statusPublished - 2011 Nov 1

Fingerprint

2-bridge Knot
Crossing number
Knot
Upper bound
Straight

Keywords

  • 2-bridge
  • Knot
  • Stick number

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Stick numbers of 2-bridge knots and links. / Huh, Youngsik; No, Sungjong; Oh, Seung Sang.

In: Proceedings of the American Mathematical Society, Vol. 139, No. 11, 01.11.2011, p. 4143-4152.

Research output: Contribution to journalArticle

Huh, Youngsik ; No, Sungjong ; Oh, Seung Sang. / Stick numbers of 2-bridge knots and links. In: Proceedings of the American Mathematical Society. 2011 ; Vol. 139, No. 11. pp. 4143-4152.
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