An Introduction to the Discharging Method

TL;DR

This survey introduces the discharging method in graph theory, explaining its principles, rules, and applications, including proofs of lemmas and an overview of the four color theorem's proof.

Contribution

It provides a comprehensive overview of the discharging method, illustrating its use through examples and explaining its role in proving key lemmas and the four color theorem.

Findings

Clarifies the principles and rules of the discharging method

Demonstrates the method's application in proving lemmas

Provides a high-level overview of the four color theorem proof

Abstract

In this survey essay, I explore the application of the discharging method in graph theory, including the selection of charging rules and discharging rules, and the general characteristics of the discharging method. As examples, I will prove some lemmas using the discharging method and provide a high-level description of the proof of the four color theorem.