colorable | colorable knot

Color each segment of a knot diagram using one of three colors. If 1. At any crossing, either the colors are all different or all the same, and 2. At least two colors are used, then a knot is said to be three-colorable (or sometimes, simply "colorable"). Colorability is invariant under Reidemeister moves, and can be generalized. For instance, for five colors 0, 1, 2, 3, and 4, a knot is five-colorable if 1. At any crossing, three segments meet. If the overpass is numbered a and the two underpasses B and C, then 2a congruent b + c (mod 5), and 2. At least two colors are used.

coloring | three-colorable graph | three-colorable map | worm