Date of Award

2016

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

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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