, Volume 44, Issue 1, pp 91-95,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 18 Mar 2009

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 S 2 and in ℝ2.

The research of J. Hass was supported in part by NSF grant DMS-0306602.