Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbid- den number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.
Crans, A., B. Mellor, and S. Ganzell, 2015: The forbidden number of a knot. Kyungpook Mathematical Journal, 55.2, 485-506, http://dx.doi.org/10.5666/KMJ.2015.55.2.485. Learn more at http://kmj.knu.ac.kr. Copyright © Department of Mathematics at Kyungpook National University.