Babai–Godsil–Imrich–Lovász conjecture on almost all Cayley graphs being GRRs

Let $R$ be a group of order $r$ that is neither abelian of exponent greater than $2$ nor generalized dicyclic. For a subset $S\subseteq R$, write $\operatorname{Cay}(R,S)$ for the Cayley digraph with vertex set $R$ and arcs $(u,v)$ whenever $vu^{-1}\in S$. If $S=S^{-1}$, this is a Cayley graph. A graphical regular representation (GRR) is a Cayley graph whose full automorphism group is $R$ acting regularly on its vertices.

Babai–Godsil–Imrich–Lovász conjecture. The proportion of inverse-closed subsets $S$ of $R$ such that $\operatorname{Cay}(R,S)$ is a GRR of $R$ approaches $1$ as $r$ approaches infinity.

The paper states that this conjecture is completely solved in the affirmative, with an explicit lower bound for the proportion and hence convergence to $1$.