Hadwiger's conjecture is one of the deepest open questions in graph theory, and Cayley graphs are an applicable and useful subtopic of algebra.
Chapter 1 will introduce Hadwiger's conjecture and Cayley graphs, providing a summary of background information on those topics, and continuing by introducing our problem. Chapter 2 will provide necessary definitions. Chapter 3 will give a brief survey of background information and of the existing literature on Hadwiger's conjecture, Hamiltonicity, and the isoperimetric number; in this chapter we will explore what cases are already shown and what the most recent results are. Chapter 4 will give our decomposition theorem about PSL2 (R). Chapter 5 will continue with corollaries of the decomposition theorem, including showing that Hadwiger's conjecture holds for our Cayley graphs. Chapter 6 will finish with some interesting examples.
| Identifer | oai:union.ndltd.org:WKU/oai:digitalcommons.wku.edu:theses-3103 |
| Date | 01 April 2018 |
| Creators | Bell, Kathleen |
| Publisher | TopSCHOLAR® |
| Source Sets | Western Kentucky University Theses |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Masters Theses & Specialist Projects |
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