Term of Award

Spring 2014

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Copyright Statement / License for Reuse

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Department

Department of Mathematical Sciences

Committee Chair

Colton Magnant

Committee Member 1

Andrew Sills

Committee Member 2

Hua Wang

Abstract

The utilization of partitions is essential for proving the properties of different types of graphs. Gallai-Ramsey problems and conjectures which require the Regularity lemma require unique methods to improve the bounds on known results. In this work the upper bounds for Gallai-Ramsey using $k$ colors is lowered to at most $k(n-1) +3n$ for even cycles and $(2^{k+3}-3)n \log n$ for odd cycles. Also, with the ideas of partitions in mind, the Regularity lemma was used to show that it is possible to create short paths with a fixed end point in hopes of pursuing the Enomoto and Ota conjecture.

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