Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Ping Zhang

Second Advisor

Dr. Gary Chartrand

Third Advisor

Dr. Allen Schwenk

Fourth Advisor

Dr. Heather Jordon


Rainbow coloring, Hamiltonian graph, Hamiltonian cycles, Hamiltonian extension, Hamiltonian digraph, proper coloring


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