A Simple Proof for the Four-Color Theorem

Abstract

The four-color theorem states that no more than four colors are required to color all nodes in planar graphs such that no two adjacent nodes are of the same color. The theorem was first propounded by Francis Guthrie in 1852. Since then, scholars have either failed to solve this theorem or required computer assistance to prove it. Hence, the goal of this paper is to provide the first correct proof of this 170-year-old mathematical problem composed with the human brain and without computer assistance in only five pages.