Maslova's conjecture on prime graphs of finite groups

Let $G$ be a finite group. Its prime graph has vertex set consisting of the prime divisors of $|G|$, with two distinct vertices adjacent when their product divides the order of some element of $G$. A 3-coclique is a set of three pairwise nonadjacent vertices. The Gruenberg–Kegel graph of a finite group is its prime graph.

Maslova's conjecture. If the prime graph of $G$ does not contain 3-cocliques, then it is isomorphic to the Gruenberg–Kegel graph of some finite solvable group.

Prime graphs of finite simple groups are known, but realizability of graphs as prime graphs of arbitrary finite groups is poorly understood. Maslova's conjecture is known for almost simple groups, while the general case remains open.