What can we hope to accomplish in generalized Ramsey theory ? (Q1092924)

Let F, G, and H denote graphs. We write \(F\to (G,H)\) to mean that, however the edges of F are colored red and blue, either the red subgraph of F contains a copy of G or the blue subgraph of F contains a copy of H. We write \(r(G,H)=t\) if \(K_ t\to (G,H)\) but \(K_{t-1}\nrightarrow (G,H)\); r(G,H) is called the Ramsey number of G and H. In this paper, the author discusses many of the major results and conjectures about Ramsey numbers and the arrow relations. He also discusses possible directions for new research in this area and adds several conjectures of his own.