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Ramsey theory is a eld of study named after the mathematician Frank P. Ramsey. In general, problems in Ramsey theory look for structure amid a collection of unstructured objects and are often solved using techniques of Graph Theory. For a typical question in Ramsey theory, we use two colors, say red and blue, to color the edges of a complete graph, and then look for either a complete subgraph of order n whose edges are all red or a complete subgraph of order m whose edges are all blue. The minimum number of vertices needed to guarantee one of these subgraphs is the Ramsey number, R(n; m). Ramsey's Theorem shows that R(n; m) exists for every n and m greater than one, yet very few Ramsey numbers are known. There are many interesting modifications of the original problem such as looking for subgraphs other than complete graphs. For this thesis, we will consider modified Ramsey numbers for star graphs instead of the classical Ramsey number R(n; m). We will prove a general formula for the modified Ramsey number of two star graphs and begin exploring modified Ramsey numbers of a star graph and a path.



Thesis Comittee

Dr. Shannon Lockard, Thesis Advisor

Dr. Rachel Stahl, Committee Member

Dr. Stephen Flood, Committee Member

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Original document was submitted as an Honors Program requirement. Copyright is held by the author.

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Mathematics Commons