A Simple Proof for the Four-Color Theorem

TL;DR

This paper presents the first human-verifiable, computer-free proof of the four-color theorem, a longstanding problem in graph theory, demonstrating that four colors suffice to color any planar graph.

Contribution

It offers a concise, human-readable proof of the four-color theorem, resolving a 170-year-old mathematical challenge without computer aid.

Findings

Proof confirms four colors are sufficient for all planar graphs

Provides a simplified, human-understandable proof structure

Eliminates the need for computer-assisted verification

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.