Havet et al.'s inversion diameter conjecture

Let $G$ be a graph, let $\operatorname{diam}(G)$ denote its inversion diameter, and let $\Delta(G)$ denote its maximum degree. Havet et al.'s inversion diameter conjecture. Every graph $G$ satisfies

$$\operatorname{diam}(G) \leq \Delta(G).$$

Havet et al. proved the weaker bound $\operatorname{diam}(G) \leq 2\Delta(G)-1$; the conjecture proposes that this bound can essentially be halved.