Publication Date

Fall 2016

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematics

First Advisor

J. Christopher Tweddle, Ph.D.

Second Advisor

Andrius Tamulis, Ph.D.

Third Advisor

Jing Zhang, Ph.D.

Abstract

The goal of this thesis is to explore the topic of graph coloring and expand on existing ideas in the field of Graph Theory. These developments will then be used to provide a possible approach in proving the 4 – color theorem that was made famous by Guthrie in the 1800’s.

Since the theorem was presented, many proofs were presented and eventually disregarded for one reason or another. Today, the types of proofs that are considered correct all rely on a computer. The first of this kind was set forth by Appel and Haken in 1977. The driving idea behind their proof was exhaustive analysis. A different approach will be taken here.

The 4 – color theorem stated is: “Any finite, planar graph can be colored using 4 (at most) colors in such a manner that no adjacent vertices will share the same color.” While a complete proof of the theorem may not be possible to complete in this thesis, an intuitive idea will be presented that has potential to be expanded on in the future.

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