Topology

An Elementary Solution of the Four-color Conjecture

Authors: Chongxi Yu
Comments: 3 Pages.

The four-color conjecture ( Guthrie's problem after F. Guthrie) is solved simply. In summary, if we choose four colors—red (Ar), blue (Bb), yellow (Ay), and green (Bg) (which can be any colors)—and divide them into Group A (Ar, Ay) and Group B (Bb, Bg); if we choose any color from Group A to color the first non-peripheral country, then to color the infinitely many countries adjacent to it, we can alternately use the two colors from the other group to color any number of countries. If the last two countries encounter the same color from the different group, then one of them must be replaced with a different color from the same group (of course, not the same color). Such a replacement only needs to occur once. The same logic applies to coloring any newly colored countries of any of the four colors, and so on, up to infinity.
Category: Topology