Tricolorability

The tricolorability of a knot refers to the ability of a knot to be colored with three colors according to two rules. In the mathematical field of knot theory, tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots.

Rules of tricolorability

A knot is tricolorable if each strand of the knot diagram can be colored one of three colors according to two rules::1. At least two colors must be used:2. At each crossing either every strand is the same color, or no color is repeated

How to color a knot

Here is an example of how to color a knot in accordance of the rules of tricolorability. By convention, knot theorists use the colors red, green, and blue.

Example of a tricolorable knot

References

* Weisstein, Eric W. "Three-Colorable Knot." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Three-ColorableKnot.html

ee also

* Fox n-coloring