Structural Ramsey Theory

A generalization of Ramsey theory to mathematical objects in which one would not normally expect structure to be found. For example, there exists a graph with very few triangles (more precisely, a graph which can always be constructed so that there is no "cycle" of triangles which are all distinct and  meets  in at least one vertex) and such that however it is colored with  colors, one of the colors contains a triangle. The usual proof of Ramsey's theorem gives no insight on how to prove such a result.