STICK NUMBERS OF 2-BRIDGE KNOTS AND LINKS

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.