Ramsey Type Results on Hypercubes and Hypergraphs

In this thesis, we will examine some Ramsey type problems for graphs and hypergraphs. Our starting point, and motivating question, is to determine the minimum number of colors required to color the edge set of a hypergraph G subject to the constraint that the edges of every copy of the hypergraph H in G receive at least q colors. We study this question in a variety of contexts for both graphs and hypergraphs. For the graph case, we focus on the situation where G is the n-dimensional hypercube and H is a hypercube, path or cycle. For the hypergraph case we consider the situation when G is a complete hypergraph and H is a complete hypergraph, path or cycle.