Unknot diagrams requiring a quadratic number of Reidemeister moves to untangle

Abstract

We present a sequence of diagrams of the unknot for which the minimum number of Reidemeister moves required to pass to the trivial diagram is quadratic with respect to the number of crossings. These bounds apply both in $S^2$ and in ${\mathbb{R}}^2$.

References in corpus (2)

• Every Reidemeister move is needed for each knot type
• Invariants of Knot Diagrams