%0 Journal Article
%T The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers
%A Yuanan Diao
%A Claus Ernst
%A Attila Por
%A Uta Ziegler
%J Mathematics
%D 2009
%I arXiv
%X For a knot or link K, let L(K) be the ropelength of K and Cr(K) be the crossing number of K. In this paper, we show that there exists a constant a>0 such that L(K) is bounded above by a Cr(K) ln^5 (Cr(K)) for any knot K. This result shows that the upper bound of the ropelength of any knot is almost linear in terms of its minimum crossing number.
%U http://arxiv.org/abs/0912.3282v1