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We show that the forbidden detour move, essentially introduced by Kanenobuand Nelson, is an unknotting operation for virtual knots. Then we define theforbidden detour number of a virtual knot to be the minimal number of forbiddendetour moves necessary to transform a diagram of the virtual knot into thetrivial knot diagram. Some upper and lower bounds on the forbidden detournumber are given in terms of the minimal number of real crossings or thecoefficients of the affine index polynomial of the virtual knot.

Forbidden detour number on virtual knot