A lifting of graphs to 3-uniform hypergraphs, its generalization, and further investigation of hypergraph Ramsey numbers

WCU Author/Contributor (non-WCU co-authors, if there are any, appear on document)
Aaron Frost Rapp (Creator)
Western Carolina University (WCU )
Web Site: http://library.wcu.edu/
Mark Budden

Abstract: Ramsey theory has posed many interesting questions for graph theorists that have yet to besolved. Many different methods have been used to find Ramsey numbers, though very feware actually known. Because of this, more mathematical tools are needed to prove exactvalues of Ramsey numbers and their generalizations. Budden, Hiller, Lambert, and Sanfordhave created a lifting from graphs to 3-uniform hypergraphs that has shown promise. Theybelieve that many results may come of this lifting, and have discovered some themselves.This thesis will build upon their work by considering other important properties of theirlifting and analogous liftings for higher-uniform hypergraphs. We also consider ways inwhich one may extend many known results in Ramsey Theory for graphs to the r-uniformhypergraph setting.

Additional Information

Language: English
Date: 2015
Graph Theory, Hypergraph Ramsey Numbers, Ramsey Numbers, Ramsey Theory
Ramsey theory
Ramsey numbers

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