Stick numbers of $2$-bridge knots and links

Youngsik Huh; Sungjong No; Seungsang Oh

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arXiv · 1411.1850

Stick numbers of $2$-bridge knots and links

Youngsik Huh·Sungjong No·Seungsang Oh

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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.

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BibTeX RIS

Youngsik Huh, Sungjong No, Seungsang Oh. 2014-11-07. Stick numbers of $2$-bridge knots and links. https://arxiv.org/abs/1411.1850

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