Author

Yuan SiFollow

Author ORCID Identifier

https://orcid.org/0000-0001-5905-0510

Date of Award

Summer 8-10-2021

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Guantao Chen

Abstract

The topics of this thesis lie in graph Ramsey theory. Given two graphs G and H, by the Ramsey theorem, there exist infinitely many graphs F such that if we partition the edges of F into two sets, say Red and Blue, then either the graph induced by the red edges contains G or the graph induced by the blue edges contains H. The minimum order of F is called the Ramsey number and the minimum of the size of F is called the size Ramsey number. They are denoted by r(G, H) and ˆr(G, H), respectively. We will investigate size Ramsey numbers involving double stars and brooms.

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