Another Proof of the Four Colour Theorem -- Part 2 -- Discharging a minimal 5-Chromatic Planar Graph

TL;DR

This paper presents a detailed, hand-checkable proof of the unavoidability of certain configurations in minimal 5-chromatic planar graphs, contributing to the four color theorem proof with a structured discharging method.

Contribution

It offers a comprehensive, structured hand-checkable proof of unavoidability in minimal 5-chromatic planar graphs, advancing the discharging approach in four color theorem proofs.

Findings

Proof of unavoidability is fully hand-checkable

Structured discharging method applied to minimal 5-chromatic graphs

Complements previous mammoth hand-checkable proofs

Abstract

In RSST, they "replace the mammoth hand-checking of unavoidability that A&H required, by another mammoth hand-checkable proof " (page 18). Here, the proof of unavoidability is accomplished in a lengthy structured hand-checkable proof whose entirety is presented in this document.