Take the tour ×  If you have a knot which has minimal crossings,
can you do a Reidemeister III move?   share|improve this
question I think there are examples where you can do this. I
think you can't do a Reidemeister move on an alternating diagram
(where if you travel along the knot you alternated over- and
under-passes), but there are knots whose minimal crossing
diagrams aren't alternating --- on such a knot, you should be
able to do a Reidemeister III. –  Gerry Myerson Jan 11 at 1:56
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