The four color problem has already been proved by Kenneth Appel and Wolfgang Haken back in 1976 (http://en.wikipedia.org/wiki/Four_color_theorem). Since it was the first major problem that required a computer to be completed, many people are still trying to find a simple and elegant, human checkable, “pencil and paper” proof of the problem … if any.
The approach used here to solve the problem is based on two results which, I think (please, please, please verify), haven’t been considered so far.
- Only maps with all faces with five or more edges can be considered when searching for a proof of the four color problem, as proved in T1 (T1 was already known by Kempe in the year 1879 – CORRECTED! 02/Apr/2011)
- All regular maps, no matter the complexity, can be topologically transformed into “circular maps” or “rectangular maps”, as proved in T2
I would really like someone to verify that the approach I used so far is correct. In computer programming it is believed that is almost impossible to find errors if you are called to test your own software and this is not different for ideas. So please help!
If you like, try the application I created to generate circular and rectangular maps … and to color them automatically. The software can be found here:
From command line, just use the java command:
- jar -jar ct-ui-swixml-VERSION-jar-with-dependencies.jar (no installation required)
Contact me for any help!