Upper Bounds for Ropelength as a Function of Crossing Number

Jason Cantarella; X. W. Faber; Chad A. Mullikin

doi:10.1016/s0166-8641(03)00168-8

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Upper Bounds for Ropelength as a Function of Crossing Number

Jason Cantarella·X. W. Faber·Chad A. Mullikin

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Abstract

The paper provides bounds for the ropelength of a link in terms of the crossing numbers of its split components. As in earlier papers, the bounds grow with the square of the crossing number; however, the constant involved is a substantial improvement on previous results. The proof depends essentially on writing links in terms of their arc-presentations, and has as a key ingredient Bae and Park's theorem that an n-crossing link has an arc-presentation with less than or equal to n+2 arcs.

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Jason Cantarella, X. W. Faber, Chad A. Mullikin. 2002-10-16. Upper Bounds for Ropelength as a Function of Crossing Number. https://doi.org/10.1016/s0166-8641(03)00168-8

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