Discrete & Computational Geometry

, Volume 44, Issue 1, pp 91–95

Unknot Diagrams Requiring a Quadratic Number of Reidemeister Moves to Untangle

Open AccessArticle

DOI: 10.1007/s00454-009-9156-4

Cite this article as:
Hass, J. & Nowik, T. Discrete Comput Geom (2010) 44: 91. doi:10.1007/s00454-009-9156-4


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.


Reidemister moves Unknot 
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© The Author(s) 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael