Francis Guthrie's approach to The Four Color Problem

TL;DR

This paper discusses Guthrie's approach to the Four Color Problem, focusing on the unique coloring properties of odd wheel graphs and their significance in understanding 4-critical graphs.

Contribution

It highlights the role of odd wheel graphs in Guthrie's approach, providing insights into the structure of 4-critical graphs related to the Four Color Problem.

Findings

Odd wheel graphs are the only 4-critical graphs with a uniquely colored vertex.

Supports Guthrie's approach by analyzing the coloring properties of odd wheel graphs.

Provides structural insights into 4-critical graphs relevant to the Four Color Problem.

Abstract

The odd wheel is the only type of 4-critical graph in which one vertex always gets a unique color. This supports Frederic Guthrie's approach to the Four Color Problem.