Quentin Dubroff, Rutgers University

Abstract

Given a coloring of the triples of some finite set by q colors, how large of a subset can one find where all triples receive the same color? The answer to this widely open question could possibly change drastically from q=2 to q=4. I'll discuss certain aspects of this hypergraph Ramsey theory problem and sketch a construction of a graph family whose Ramsey number provably depends significantly on the number of colors used. Time and interest permitting, I'll discuss one or two numerical curiosities that might underlie a conspiracy at the heart of Ramsey theory.