Connected forcing number lower bound conjecture

Let $G$ be a connected graph with minimum degree $\delta$ and girth $g$, and let $F_c(G)$ denote its connected forcing number.

Connected forcing number lower bound conjecture.

$$F_c(G) \ge \delta + (\delta - 2)(g - 3).$$

This is a weaker version of the original lower-bound conjecture for the forcing number $F(G)$, because $F(G) \le F_c(G)$. The original conjecture remains open, and this connected-forcing version is presented as an open problem.