Theory on the Structure and Coloring of Maximal Planar Graphs (1)Recursion Formulae of Chromatic Polynomial and Four-Color Conjecture

TL;DR

This paper introduces recursion formulae for the chromatic polynomial of maximal planar graphs and explores their application in proving the Four-Color Conjecture, focusing on a special class of graphs.

Contribution

It presents new recursion formulae for chromatic polynomials and applies them to advance the proof of the Four-Color Conjecture.

Findings

Recursion formulae for chromatic polynomial of maximal planar graphs

Application of formulae to Four-Color Conjecture proof

Focus on 4-chromatic-funnel pseudo uniquely-4-colorable graphs

Abstract

In this paper, two recursion formulae of chromatic polynomial of a maximal planar graph G are obtained. Moreover, the application of these formulaes to the proof of Four-Color Conjecture is investigated. By using these formulae, the proof of Four-Color Conjecture boils down to the study on a special class of graphs, viz., 4-chromatic-funnel pseudo uniquely-4-colorable maximal planar graphs.