AN UPPER BOUND ON STICK NUMBER OF KNOTS

초록

In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) <= 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) <= 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) <= 3/2 c(K).

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