Dense regular Maxwell-sharpness conjecture

Prove that every k-regular n-vertex graph with k≥(3n−6)/4 is Maxwell-sharp, meaning that its rigidity dimension equals its Maxwell dimension.

Background

This conjecture is the regular dense specialization of the broader Krivelevich–Lew–Michaeli minimum-degree conjecture. Maxwell’s edge-count condition is automatically paired with the relevant connectivity condition in this degree range, but the sufficiency of these conditions remains unresolved beyond the cases proved in the paper.