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arXiv · 1711.10975

The first order convergence law fails for random perfect graphs

Tobias Müller·Marc Noy
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Abstract

We consider first order expressible properties of random perfect graphs. That is, we pick a graph $G_n$ uniformly at random from all (labelled) 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 $n\to\infty$.

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Tobias Müller, Marc Noy. 2018-10-01. The first order convergence law fails for random perfect graphs. https://arxiv.org/abs/1711.10975

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