On the probability of planarity of a random graph near the critical point

Marc Noy, Vlady Ravelomanana, Juanjo Rué

Consider the uniform random graph $G(n,M)$ with $n$ vertices and $M$ edges. Erdős and Rényi (1960) conjectured that the limit $$ \lim_{n \to \infty} \Pr\{G(n,\textstyle{n\over 2})…