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Explorations in Topology by David Gay

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5

How to Color a Map with Four Colors

This is a historical chapter. The chapter’s bulk is the “proof” of the four-color theorem for maps on the sphere due to Kempe in 1879. This gives readers an experience of the first, serious attempt at a proof the four-color theorem. In the end-of-chapter investigations, readers are given the opportunity of “discovering” counterexamples to Kempe’s proof, thus exposing the error in his argument. The end-of-chapter notes section sketches a summary of the history of the problem from Kempe on. Two main events are discussed. First, the discovery of a counterexample to Kempe by Heawood in 1890. Second, the controversial, but widely accepted, proof in 1976 by Appel and Haken. This proof provides a focus for a broader ...

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