Liu–Zhang's edge bound in terms of maximum forcing number

Let $G$ be a finite simple graph of order $2n$ with a perfect matching. Write $e(G)$ for the number of edges of $G$, and let $F(G)$ denote its maximum forcing number. Liu–Zhang's conjecture. The graph $G$ satisfies

$$e(G)\geq \frac{n^2}{n-F(G)}, \text{ equivalently, } F(G)\leq n-\frac{n^2}{e(G)}.$$

This conjecture proposes an improved lower bound on the number of edges in terms of the maximum forcing number; the supplied source does not indicate whether it has been resolved.