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.
Recommended Citation
Armstrong, Addie, "Degree-Limited Defective Three Colorings of Planar Graphs Containing No 4-Cycles or 5-Cycles" (2016). Open Access Dissertations. Paper 435.
https://digitalcommons.uri.edu/oa_diss/435
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