We give a partial answer to the following question of Dobrinen: For a given topological Ramsey space R, are the notions of selective for R and Ramsey for R equivalent? Every topological Ramsey space R has an associated notion of Ramsey ultrafilter for R and selective ultrafilter for R (see [1]). If R is taken to be the Ellentuck space then the two concepts reduce to the familiar notions of Rams...

We prove the Ramsey property of classes of ordered structures with closures and given local properties. This generalises earlier results: the Nešetřil-Rödl Theorem, the Ramsey property of partial orders and metric spaces as well as the author’s Ramsey lift of bowtiefree graphs. We use this framework to give new examples of Ramsey classes. Among others, we show (and characterise) the Ramsey prop...

Graham, Jan Karel Lenstra, and Robert E. Tarjan Discrete.This article is about the large number named after Ronald Graham. While Graham was trying to explain a result in Ramsey theory which he had derived with his collaborator Bruce Lee. Ramseys Theorem for n-Parameter Sets PDF.on Ramsey theory. Szemerédis most famous theorem is at the heart of Ramsey theory. Graham is the informal administrato...

Let (T1, T2, . . . , Tc) be a fixed c-tuple of sets of graphs (i.e. each Ti is a set of graphs). Let R(c, n, (T1, T2, . . . , Tc)) denote the set of all n-tuples, (a1, a2, . . . , an), such that every c-coloring of the edges of the complete multipartite graph, Ka1,a2,...,an , forces a monochromatic subgraph of color i from the set Ti (for at least one i). If N denotes the set of non-negative in...