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.
Identifer | oai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-4050 |
Date | 01 June 2022 |
Creators | Lai, David |
Publisher | DigitalCommons@CalPoly |
Source Sets | California Polytechnic State University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Master's Theses |
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