The FKKR upper-bound conjecture for identifying codes

Let $G$ be a twin-free graph, let $|V(G)|$ denote its number of vertices, and let $amma^{\text{\tiny{ID}}}(G)$ be its identifying code number. Write $\Delta(G)$ for the maximum degree of $G$. FKKR upper-bound conjecture. There exists a constant $c$ such that for every twin-free graph $G$,

$$\gamma^{\text{\tiny{ID}}}(G) \leq |V(G)|- \frac{|V(G)|}{\Delta(G)}+c.$$

This conjecture proposes an upper bound improving the general bound $\gamma^{\text{\tiny{ID}}}(G)\leq |V(G)|-1$ in terms of the order and maximum degree of the graph. The supplied text gives no evidence that the conjecture has been resolved.