Let χc(H) denote the circular chromatic number of a graph H. For graphs F and G, the circular chromatic Ramsey number Rχc(F,G) is the infimum of χc(H) over graphs H such that every red/blue edge-coloring of H contains a red copy of F or a blue copy of G. We characterize Rχc(F,G) in terms of a Ramsey problem for the families of homomorphic images of F and G. Letting zk = 3 − 2 −k, we prove that ...

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii PRELIMINARIES AND NOTATION . . . . . . . . . . . . . . . . . . . . . ix CHAPTER 1. OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 The Graph Ramsey Number . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Arrow Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 The Dir...