Stick numbers of $2$-bridge knots and links

Youngsik Huh; Sungjong No; Seungsang Oh

Stick numbers of $2$-bridge knots and links

Geometric Topology 2014-11-10 v1

Authors: Youngsik Huh , Sungjong No , Seungsang Oh

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 $s(K) \leq 2 c(K)$ . Furthermore McCabe proved $s(K) \leq c(K) + 3$ for a $2$ -bridge knot or link, except in the case 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.

Keywords

stick number 2-bridge knots links crossing number upper bound straight sticks hopf link

Cite

@article{arxiv.1411.1850,
  title  = {Stick numbers of $2$-bridge knots and links},
  author = {Youngsik Huh and Sungjong No and Seungsang Oh},
  journal= {arXiv preprint arXiv:1411.1850},
  year   = {2014}
}

Stick numbers of $2$-bridge knots and links

Abstract

Keywords

Cite

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