On Algebraic Knots II : An upper bound on their ropelength(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

Abstract

We prove that given a Conway algebraic link diagram D with n crossings then D can be embedded on the cubic lattice with a length bounded above by cn, where c is a positive constant independent of D and n. This implies that the ropelength of alternating Conway algebraic knots growths at most linear with their crossing number.