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Kempe Chain

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Mathematicians offer fresh proof of the Four-Color Theorem

A new mathematical proof revisits the long-standing four-color theorem, which states that any map can be colored with just four colors so no adjacent regions share one. The proof builds on the historical lineage from Alfred Kempe's flawed 19th-century attempt, later fixed conceptually through Kempe chains, and the 1976 computer-assisted proof by Kenneth Appel and Wolfgang Haken that checked thousands of configurations.