The forbidden number of a knot
arXiv:1305.5200
Abstract
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 {\it forbidden number}. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.
14 pages, many figures; v2 improves the upper bounds from the crossing number, and adds more detail to the data presented in the conclusion