Random subgraphs of finite graphs: III. The phase transition for the $n$-cube

Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad +2

We study random subgraphs of the $n$-cube $\{0,1{\}}^n$, where nearest-neighbor edges are occupied with probability $p$. Let $p_c(n)$ be the value of $p$ for which the expected clust…