Converse relationship between the derangement-graph question and the Praeger–Neumann conjecture

Determine whether the Neumann–Praeger conjecture follows conversely from a positive answer to Question 6.1 concerning degree bounds for transitive permutation groups whose derangement graphs lack a prescribed clique.

Background

The paper records a known implication: a positive answer to the derangement-graph question on bounding the degree of a transitive group without a k-clique would imply the Praeger–Neumann conjecture on covering subgroups.

The converse implication is explicitly identified as unresolved. This is distinct from the main theorem of the paper, which proves the Neumann–Praeger conjecture only in the case where the normal subgroup has index 3.