Five color theorem

Common card · No. 402338

The five color theorem is a result from graph theory that given a plane separated into regions, such as a political map of the countries of the world, the regions may be colored using no more than five colors in such a way that no two adjacent regions receive the same color. Adjacent means that two regions share a common boundary of non-zero length (i.e., not merely a corner where three or more regions meet). The five color theorem is implied by the stronger four color theorem, but is considerably easier to prove. It was first proved by Percy John Heawood in 1890, based on a purported proof of the four color theorem given by Alfred Kempe in 1879. That proof had been considered correct for 11 years, but Heawood found an error in it; he did manage to give a correct proof of the weaker five color theorem, based on Kempe's work. The first correct proof of the four color theorem was found only in 1976.

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