tricolorability

thumb|right|A tricolored trefoil knot.In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots. In particular, since the unknot is not tricolorable, any tricolorable knot is necessarily nontrivial.

==Rules of tricolorability== In these rules a strand in a knot diagram will be a piece of the string that goes from one undercrossing to the next. A knot is tricolorable if each strand of the knot diagram can be colored one of three colors, subject to the following rules: 1. At least two colors must be used, and 2. At each crossing, the three incident strands are either all the same color or all different colors.