The Four Color Theorem states that 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. https://en.wikipedia.org/wiki/Four_color_theorem

Computational tests, checking millions of possible configurations, have never found an exception. But as yet, there isn't any formal mathematical proof of this. (note that a formal proof with 5 colors was made in the late 19th century (Heawood 1890) https://en.wikipedia.org/wiki/Percy_John_Heawood

Share this page