Open Access Thesis
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
Master of Arts
Department of Mathematics
Adrienne Stanley, Chair, Thesis Committee
1 PDF file (viii, 39 pages)
©2020 Jake Weber
Weber, Jake, "An exploration in Ramsey theory" (2020). Dissertations and Theses @ UNI. 1022.