The Hamiltonicity conjecture for the wiggly flip graph

Let $\mathrm{WFG}_n$ be the wiggly flip graph. Hamiltonicity conjecture. The wiggly flip graph $\mathrm{WFG}_n$ admits a Hamiltonian path, or even a Hamiltonian cycle. The authors checked this conjecture computationally for $n\leq 3$. Its validity for general $n$ remains open.