TITLE: Unknotting number of knot diagrams
QUESTION [9 upvotes]: Define the "diagram unknotting number" of a knot diagram $D$ as the minimal number of crossings that need to be changed in $D$ in order to get a diagram of the trivial knot (the usual unknotting number of  a knot $K$ is the minimum over the diagram unknotting numbers of its diagrams).
Can you give me an example of a diagram of the trefoil knot (or any other knot having unknotting number = 1) with diagram unknotting number greater than 1?

REPLY [5 votes]: You should check this paper.
http://arxiv.org/abs/0805.3174
http://www.worldscientific.com/doi/abs/10.1142/S0218216509007361