The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the counties of a state, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color.
The five color theorem is implied by the stronger four color theorem, but is considerably easier to prove. It was based on a failed attempt at the four color proof by Alfred Kempe in 1879. Percy John Heawood found an error 11 years later, and proved the five color theorem based on Kempe's work. The four color theorem was finally proven by Kenneth Appel and Wolfgang Haken at the University of Illinois, with the aid of a computer. They were assisted in some algorithmic work by John A. Koch.
Read more about Five Color Theorem: Outline of The Proof By Contradiction, Linear Time Five-coloring Algorithm
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