Stick numbers of 2-bridge knots and links

Huh, Youngsik; No, Sungjong; Oh, Seungsang

doi:10.1090/S0002-9939-2011-10832-3

Stick numbers of $2$-bridge knots and links
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by Youngsik Huh, Sungjong No and Seungsang Oh PDF

Proc. Amer. Math. Soc. 139 (2011), 4143-4152 Request permission

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 that $s(K) \leq c(K) + 3$ 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.

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