DOI: https://doi.org/10.15368/theses.2022.41
Available at: https://digitalcommons.calpoly.edu/theses/2621
Date of Award
6-2022
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Anthony Mendes
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
The Ramsey number $R(r, b)$ is the least positive integer such that every edge 2-coloring of the complete graph $K_{R(r, b)}$ with colors red and blue either embeds a red $K_r$ or a blue $K_b$. We explore various methods to find lower bounds on $R(r,b)$, finding new results on fibrations and semicirculant graphs. Then, generalizing the Ramsey number to graphs other than complete graphs, we flesh out the missing details in the literature on a theorem that completely determines the generalized Ramsey number for cycles.