An upper bound on stick numbers of knots

Abstract

In 1991, 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 $s(K)\le 2c(K)$. In this paper we improve this upper bound to $s(K)\le \frac{3}{2}(c(K)+1)$. Moreover if $K$ is a non-alternating prime knot, then $s(K)\le \frac{3}{2}c(K)$.

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