Ribbonlength and crossing number for folded ribbon knots.

We study Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot. We show for any knot or link type that there exist constants c 1 , c 2 > 0 such that the ribbonlength is bounded above by c 1 Cr (K) 2 , and also by c 2 Cr (K) 3 / 2 . We use a different method for each bound. The constant c 1 is quite small in comparison to c 2 , and the first bound is lower than the second for knots and links with Cr (K) ≤ 12,748. [ABSTRACT FROM AUTHOR]