Rafla's conjecture on crossing-free Hamiltonian cycles in simple drawings

Let $K_n$ be the complete graph, and let a simple drawing be a drawing in which any two edges have at most one common point and no two edges incident to the same vertex cross. A crossing-free Hamiltonian cycle is a cycle that visits every vertex exactly once and whose edges do not cross. Rafla's conjecture. Every simple drawing of $K_n$ with $n \geq 3$ vertices contains a crossing-free Hamiltonian cycle.

This conjecture asks whether the familiar property of straight-line drawings of complete graphs extends to all simple drawings. It was conjectured by Rafla in 1988; the supplied text gives no evidence of a general resolution, although it records proofs for several restricted drawing classes.