Dissertations and Theses @ UNI
Availability
Open Access Thesis
Keywords
Ramsey theory;
Abstract
We present several introductory results in the realm of Ramsey Theory, a subfield of Combinatorics and Graph Theory. The proofs in this thesis revolve around identifying substructure amidst chaos. After showing the existence of Ramsey numbers of two types, we exhibit how these two numbers are related. Shifting our focus to one of the Ramsey number types, we provide an argument that establishes the exact Ramsey number for h(k, 3) for k ≥ 3; this result is the highlight of this thesis. We conclude with facts that begin to establish lower bounds on these types of Ramsey numbers for graphs requiring more substructure.
Year of Submission
5-2020
Degree Name
Master of Arts
Department
Department of Mathematics
First Advisor
Adrienne Stanley, Chair, Thesis Committee
Date Original
5-8-2020
Object Description
1 PDF file (viii, 39 pages)
Copyright
©2020 Jake Weber
Language
en
File Format
application/pdf
Recommended Citation
Weber, Jake, "An exploration in Ramsey theory" (2020). Dissertations and Theses @ UNI. 1022.
https://scholarworks.uni.edu/etd/1022
