Caleb Fong, Rutgers University

Abstract

For various examples of a graph H, an interesting question to ask is how big an H-intersecting family of graphs on n vertices can be, where H-intersecting means any two members of the family contain H (as a subgraph) in their intersection. An early instance of this problem is for H = K_3, with entropic upper bounds given by Chung--Frankl--Graham--Shearer, ultimately tightened to best possible by Ellis--Filmus--Friedgut using Fourier-analytic methods. We will also consider the question for general H = K_t,  for H = Hamiltonian cycle, and for H = connected.