The genus of the Erdős-Rényi random graph and the fragile genus property

Chris Dowden, Mihyun Kang, Michael Krivelevich

We investigate the genus $g(n,m)$ of the Erdős-Rényi random graph $G(n,m)$, providing a thorough description of how this relates to the function $m=m(n)$, and finding that there is…