A Key to Proof of 4-Color Theorem
QU Zi-pu · 2004
the crucial reason why the 4-color problem has not been solved for hundred years lies in a simplifying problem fails to be resolved. The simplifying problem posed by A.Kempe refers that in the unavoidable structures group, a so-called simplifying problem cannot be solved which happens in the case of that a country or region has five neighboring countries or regions. Mathematical induction was used to proof the 4-color theorem, while vertex-coloring on a planar graph (to be issued) does not need to use induction. However both of the methods refer to a main point that a vertex to be colored has five adjacent vertices that are respectively colored 4 colors and the matter is how to free up one color from the four colors to color the vertex. This is also a key to proof the 4-color theorem. So this paper aims to further make the key clear according to the method of interchanging colors to complete the two papers written before. And the steps of interchanging colors are 6 steps at most.