Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle

Given any knot diagram E, we present a sequence of knot diagrams of the same knot type, for which the minimum number of Reidemeister moves required to pass to E is quadratic with respect to the number of crossings. These bounds apply both in S2 and in R2 .

• Type: Journal
• Year: 2010
• Where: DCG
• Authors: Joel Hass, Tahl Nowik
• Keywords: DCG 2008, DCG 2010, Knot Diagrams, Knot Type, Minimum Number