Tricolorability

Summary

A knot is tricolorable if the arcs of a diagram can be colored with three colors under a simple rule. At each crossing the three meeting arcs must show one color or all three colors, and at least two colors must appear. Whether this is possible does not depend on the chosen diagram, so tricolorability is a property detected by a knot invariant. It is the simplest tool to prove that a knot is really knotted.