A Simple Proof of the Four-Color Theorem

الأصل · EN

A simpler proof of the four color theorem is presented. The proof was reached using a series of equivalent theorems. First the maximum number of edges of a planar graph is obatined as well as the minimum number of edges for a complete graph. Then it is shown that for the theorem to be false there must exist a complete planar graph of h edges such that h>4. Finally the theorem is proved to be true by showing that there does not exist a complete planar graph with h>4.