Quentin Dubroff, Rutgers University

Abstract

How many edges can an n-vertex graph have if it contains no copy of a cycle on 4 vertices? A nice and simple argument shows that the answer is at most 10n^{3/2}, but is this a good upper bound? I'll describe how one might find the algebraic construction showing that it is, and then I'll survey how similar constructions can (or cannot) be used for related problems.