The Braid Indices of the Reverse Parallel Links of Alternating Knots

May 24, 2023
The braid indices of most links remain unknown as there is no known universal method that can be used to determine the braid index of an arbitrary knot. This is also the case for alternating knots. In this paper, we show that if K is an alternating knot, then the braid index of any reverse parallel link of K can be precisely determined. The formula can be easily obtained from any reduced alternating diagram D of K. As a consequence of this result, we can now prove that the ropelength of any alternating knot is at least proportional to its minimum crossing number.