On the bridge number of knot diagrams with minimal crossings

Jae-Wook Chung, Xiao-Song Lin

Given a diagram $D$ of a knot $K$, we consider the number $c(D)$ of crossings and the number $b(D)$ of overpasses of $D$. We show that, if $D$ is a diagram of a nontrivial knot $K$…