A formal proof of the four color theorem

Abstract

A formal proof has not been found for the four color theorem since 1852 when Francis Guthrie first conjectured the four color theorem. Why? A bad idea, we think, directed people to a rough road. Using a similar method to that for the formal proof of the five color theorem, a formal proof is proposed in this paper of the four color theorem, namely, every planar graph is four-colorable. The formal proof proposed can also be regarded as an algorithm to color a planar graph using four colors so that no two adjacent vertices receive the same color.