Date of Award

2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Nancy Eaton

Abstract

This dissertation explores and advances results for several variants on a long-open problem in graph coloring. Steinberg's conjecture states that any planar graph containing no 4-cycles or 5-cycles is 3-colorable. The conjecture has remained open for more than forty years and brought a great deal of interest to coloring planar graphs with certain structural restrictions. In this dissertation, we present a new type of defective graph coloring that allows us to prove two main results advancing the state of Steinberg's conjecture.

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