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.

**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.

© 1996-9

1999-05-26