The Erdős–Rényi random graph maximum likelihood threshold conjecture

Let $G$ be a random graph generated according to the Erdős–Rényi model $G(n,c/n)$, where $c$ is a fixed positive real number, and let $d$ be the minimum integer such that $G$ is $d$-independent. Maximum likelihood threshold conjecture. The maximum likelihood threshold of $G$ is $d+1$ with high probability. This conjecture predicts that the upper bound for maximum likelihood thresholds is sharp for Erdős–Rényi random graphs; it is supported by computational experiments, but no resolution is given here.