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A projection of a Link is tricolorable if each of the strands in the projection can be colored in one of three different colors such that, at each crossing, all three colors come together or only one does and at least two different colors are used. The Trefoil Knot and trivial 2-link are tricolorable, but the Unknot, Whitehead Link, and Figure-of-Eight Knot are not.
If the projection of a knot is tricolorable, then Reidemeister Moves on the knot preserve tricolorability, so either every projection of a knot is tricolorable or none is.