Date of Award
6-2017
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Dr. Ping Zhang
Second Advisor
Dr. Gary Chartrand
Third Advisor
Dr. Allen Schwenk
Fourth Advisor
Dr. Heather Jordon
Keywords
Rainbow coloring, Hamiltonian graph, Hamiltonian cycles, Hamiltonian extension, Hamiltonian digraph, proper coloring
Abstract
A cycle that contains every vertex of a graph or digraph is a Hamiltonian cycle. A graph or digraph containing such a cycle is itself called Hamiltonian. This concept is named for the famous Irish physicist and mathematician Sir William Rowan Hamilton. These graphs and digraphs have been the subject of study for over six decades. In this dissertation, we study graphs and digraphs with even stronger Hamiltonian properties, namely highly Hamiltonian graphs and digraphs.
Access Setting
Dissertation-Open Access
Recommended Citation
Bi, Zhenming, "Highly Hamiltonian Graphs and Digraphs" (2017). Dissertations. 3143.
https://scholarworks.wmich.edu/dissertations/3143