Mathematics, Department of
Department of Mathematics: Dissertations, Theses, and Student Research
Accessibility Remediation
If you are unable to use this item in its current form due to accessibility barriers, you may request remediation through our remediation request form.
First Advisor
Stephen G. Hartke
Date of this Version
5-2014
Document Type
Dissertation
Abstract
This thesis focuses on determining when a graph with additional structure contains certain subgraphs, particularly circuits, cycles, or trees. The specific problems and presented results include a blend of many fundamental graph theory concepts such as edge-coloring, routing problems, decomposition problems, and containing cycles of various lengths. The three primary chapters in this thesis address the problems of finding eulerian circuits with additional restrictions, decomposing the edge-colored complete graph K_n into rainbow spanning trees, and showing a 4-connected claw-free and N(3,2,1)-free graph is pancyclic.
Adviser: Stephen G. Hartke
Comments
A dissertation Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfilment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professor Stephen G. Hartke. Lincoln, Nebraska: May, 2014
Copyright (c) 2014 James Carraher