Abstract
A class of simple undirected graphs is small if it contains at most n!α^n labeled graphs with n vertices, for some constant α. We prove that for any constants c,ε>0, the class of graphs with expansion bounded by the function f(r)=c^r^(1/3−ε) is small.
Also, we show that there exists a constant c such that the class of graphs with expansion bounded by c^r^(1/2) is not small.