2014/11/07 by Huh, Youngsik, No, Sungjong, Oh, Seungsang · 1 citation
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1411.1850
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) ≤ 2 c(K). Furthermore McCabe proved s(K) ≤ 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.