  Let $A \in \mathbb{R}^{n \times n}$ be the adjacency matrix of an Erd\H{o}s
R\'enyi graph $G(n, d/n)$ for $d = \omega(1)$ and $d \leq 3\log(n)$. We show
that as $n$ goes to infinity, with probability that goes to $1$, the adjacency
matrix of the $3$-core of $G(n, d/n)$ is invertible.
