This thesis investigates problems in a number of deterrent areas of graph theory. These problems are related in the sense that they mostly concern the coloring or structure of the underlying graph.The first problem we consider is in Ramsey Theory, a branch of graph theory stemming from the eponymous theorem which, in its simplest form, states that any esuriently large graph will contain a clique or anti-clique of a spiced size. The problem of ending the minimum size of underlying graph which will guarantee such a clique or anti-clique is an interesting problem in its own right, which has received much interest over the last eighty years but which is notoriously intractable. We consider a generalization of this problem. Rather than edges being present or not present in the underlying graph, each is assigned one of three possible colors and, rather than considering cliques, we consider cycles. Combining regularity and stability methods, we prove an exact result for a triple of long cycles.