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Ramsey Theory

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.

Identiferoai:union.ndltd.org:CALPOLY/oai:digitalcommons.calpoly.edu:theses-4050
Date01 June 2022
CreatorsLai, David
PublisherDigitalCommons@CalPoly
Source SetsCalifornia Polytechnic State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceMaster's Theses

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