Date of Award
8-1-2020
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Statistics
First Advisor
Guantao Chen
Second Advisor
Zhongshan Li
Third Advisor
Songling Shan
Fourth Advisor
Hendricus Van der Holst
Fifth Advisor
Yi Zhao
Abstract
The graph edge coloring problem is to color the edges of a graph such that adjacent edges receives different colors. Let $G$ be a simple graph with maximum degree $\Delta$. The minimum number of colors needed for such a coloring of $G$ is called the chromatic index of $G$, written $\chi'(G)$. We say $G$ is of class one if $\chi'(G)=\Delta$, otherwise it is of class 2. A majority of edge coloring papers is devoted to the Classification Problem for simple graphs. A graph $G$ is said to be \emph{overfull} if $|E(G)|>\Delta \lfloor |V(G)|/2\rfloor$. Hilton in 1985 conjectured that every graph $G$ of class two with $\Delta(G)>\frac{|V(G)|}{3}$ contains an overfull subgraph $H$ with $\Delta(H)=\Delta(G)$. In this thesis, I will introduce some of my researches toward the Classification Problem of simple graphs, and a new approach to the overfull conjecture together with some new techniques and ideas.
DOI
https://doi.org/10.57709/18310496
Recommended Citation
Cao, Yan, "Graph edge coloring and a new approach to the overfull conjecture." Dissertation, Georgia State University, 2020.
doi: https://doi.org/10.57709/18310496
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