A non-constructive proof of the Four Colour Theorem

TL;DR

This paper presents a non-constructive proof of the Four Colour Theorem using advanced combinatorial and analytical methods involving generating functions, hypergeometric series, and Tutte's enumeration of planar maps.

Contribution

It introduces a novel non-constructive proof of the Four Colour Theorem based on singularity analysis and hypergeometric functions, expanding the theoretical understanding of graph coloring.

Findings

Proof confirms the Four Colour Theorem without constructive algorithms

Utilizes singularity analysis of generating functions for triangulations

Connects hypergeometric series properties with planar map enumeration

Abstract

The approach is through a singularity analysis of generating functions for 3- and 4-connected triangulations, asymptotic analysis, properties of the ${{}_3F_2}$ hypergeometric series, and Tutte's enumerative work on planar maps and chromatic polynomials.