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 colortheorem 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 same,no pure mathematical proof is in sight.Now I give in my paper such a pure mathematical proof.