The 5 Colour Theorem

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" summary

A concise, constructive proof that any planar map requires at most five colors, using proof by induction and the Kempe-style idea of swapping along alternating color chains. The argument isolates a degree‑≤5 region, shows how swapping colors on chains lets a sixth color be eliminated, and uses planarity to prove two required chains cannot coexist. Notes the four‑color theorem needed checking of 1834 cases by computer, while this five‑color proof fits on one A4 page.

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" chapters (3)

1. 0:00Introduction
2. 1:15The 5 Colour Theorem
3. 2:20Inductive Proof

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