A Pure Mathematical Proof Of The Four Color Problem

Abstract

As stated originally the four – color problem asked whether it is always possible to color the regions of a plane map with four colors such that regions which share a common boundary ( and not just a point ) receive different colors. In the long and arduous history of attacks to prove the four color theorm many attempts came close, but what finally succeeded in the Apple – Haken proof of 1976 and also in the recent proof of Robertson ,Sanders , Seymour and Thomas 1997 was a combination of some old ideas and the calculating powers of modern – day computers. Thirty years after the original proof, the situation is still basically the the same,no pure mathematical proof is in sight.Now I give in my paper such a pure mathematical proof.