The human proof and algorithm for Four-Color Theorem
This paper presents a simple human proof of the Narrow Four-Color Theorem “Given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color, and all the outermost countries use no more than three colors. (Please refer to “Concept” for the meaning of “outermost countries”)” . And in this proof also shows the algorithm for Four-Color Maps. This paper is from a new way, from first principle (the basic and simple facts) to the final result. Concept Outermost countries countries adjacent to the infinite plane (refer to below photo, the countries highlight in yellow color) The Map means the Map that all countries in one continent. I will prove situation for only one continent map in the paper. For the separate continents, if the theorem holds, for each continent, the theorem also holds, we can let 4 the colors of outermost countries for each ...