Meagher–Razafimahatratra–Spiga conjecture on derangement graphs of even-degree groups

Let $n$ be an even integer that is not a power of $2$. A transitive permutation group $G$ of degree $n$ has derangement graph $\Gamma_G$.

Meagher–Razafimahatratra–Spiga's conjecture. There exists a transitive permutation group $G$ of degree $n$ such that $\Gamma_G$ is a complete multipartite graph with $n/2$ parts.

This conjecture concerns the existence of transitive permutation groups whose derangement graphs have a highly structured complete multipartite form. It was posed as the main motivation for the paper; the supplied text gives no evidence of resolution.