Date of Award

5-2024

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Deepak Bal

Committee Member

Jonathan Cutler

Committee Member

Aihua Li

Abstract

Given an integer n ≥ 1, the balanced double star Sn,n is a tree consisting of two vertex disjoint stars with n leaves each, connected at their central vertices by an edge. Given r ≥ 2, we consider the problem of finding the smallest integer N such that every r-colored complete bipartite graph KN,N contains a monochromatic copy of the balanced double star Sn,n. This question is an instance of a problem within Ramsey theory. In this thesis, we cover the history of Ramsey theory and our problem in general, provide an alternative approach to prove the two colored case, prove new bounds as well as exact values when r = 3, and prove new bounds for r > 3.

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