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A Simple Proof of the Four-Color Theorem

Fayez A. Alhargan
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Abstract

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 $h>4$.

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Fayez A. Alhargan. 2002-07-06. A Simple Proof of the Four-Color Theorem. https://arxiv.org/abs/math/0207061

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