Mathias Schacht, Yale University

Abstract

We consider quantitative aspects of a Ramsey theoretic result of Leeb. Leeb showed that any sufficiently large complete k-uniform hypergraph with ordered vertex set and ordered edge set must contain one of k!2^k "canonical" subhypergraphs on a given number (say m) of vertices. We obtain estimates for the corresponding Ramsey numbers. In particular, we show that for graphs these Ramsey numbers grow doubly exponential in m. For general hypergraphs the obtained lower and upper bound differ in the height of the tower functions by 2.

This is joint work with M. Tadeu Sales, Chr. Reiher, and V. Rödl.