MS Defense: A Pedagogical Approach to Problems in Ramsey Theory

Research often relies on the use of cutting edge techniques involving complicated constructions to solve problems. With a major focus on optimization and stating results as succinctly as possible, the problem solving process is frequently concealed. We believe it can be equally valuable to understand these methods when approaching research tasks. To demonstrate this, we explore several problems in graph coloring centering around the concept of Ramsey Multiplicity. We build up from simple results with loose bounds to general theorems and tighter bounds, all while keeping in mind our objective of educating the reader as to how these results are obtained instead of simply stating and proving theorems. Our work culminates in a method of deriving a general non-trivial, though sub-optimal, bound for the Ramsey Multiplicity constants in a way that could be taught in any theory class to upper level undergraduate or graduate students.

Examining Committee

Chair:

Dr. William Gasarch

Members:

Dr. Clyde Kruskal

Dr. Lawrence Washington