ABSTRACT
In this chapter, we will survey graph (and hypergraph) problems of Paul Erdõs (often with his collaborators) arising out of his work in Ramsey theory. The guiding philosophy of this subject deals with the inevitable occurrence of specific structures in some part of a large arbitrary structure which has been partitioned into finitely many parts. Well-known examples are the Pigeonhole Principle, van der Waerden's theorem on arithmetic progressions, and Ramsey's theorem itself. We will say more about these examples in subsequent sections.
