The first order convergence law fails for random perfect graphs. Issue 4 (29th October 2018) - Müller, Tobias; Noy, Marc
Abstract : We consider first order expressible properties of random perfect graphs. That is, we pick a graph G n uniformly at random from all (labeled) perfect graphs on n vertices and consider the probability that it satisfies some graph property that can be expressed in the first order language of graphs. We show that there exists such a first order expressible property for which the probability that G n satisfies it does not converge as n → ∞ .