We study Kauffman's model of folded ribbon knots: knots made a thin strip paper flat in the plane. The ribbonlength is length to width ratio such knot. show for any knot or link type that there exist constants $c_1, c_2>0$ bounded above by $c_1\cdot Cr(K)^2$, and also $c_2\cdot Cr(K)^{3/2}$. use different method each bound. constant $c_1$ quite small comparison $c_2$, first bound lower than sec...

Reducing the number of link crossings in a network drawn on plane such as wiring board is well-known problem, and especially calculation minimum crossings: this crossing problem. It has been shown that finding general solution to problem NP-hard. So, addressed for particular classes graphs also our approach paper. More precisely, we focus hereinafter torus topology. First, discuss an upper boun...