To color any map on the sphere or the plane requires at most six-colors. This number can easily be reduced to five, and the four-color theorem demonstrates that the necessary number is, in fact, four.
Six-Color Theorem
See also
Four-Color Theorem, Heawood Conjecture, Map ColoringExplore with Wolfram|Alpha
References
Franklin, P. "A Six Colour Problem." J. Math. Phys. 13, 363-369, 1934.Hoffman, I. and Soifer, A. "Another Six-Coloring of the Plane." Disc. Math. 150, 427-429, 1996.Saaty, T. L. and Kainen, P. C. The Four-Color Problem: Assaults and Conquest. New York: Dover, 1986.Referenced on Wolfram|Alpha
Six-Color TheoremCite this as:
Weisstein, Eric W. "Six-Color Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Six-ColorTheorem.html