The cover-to-domination cover pebbling ratio conjecture

Let $G$ be a graph with more than one vertex. Write $\lambda(G)$ for its cover pebbling number and $\psi(G)$ for its domination cover pebbling number. Cover-to-domination cover pebbling ratio conjecture. The ratio $\lambda(G)/\psi(G)$ should satisfy

$$\frac{\lambda(G)}{\psi(G)}\geq 3.$$

The paper notes that this bound is attained by the complete graph on two vertices and that graph families can make the ratio arbitrarily close to $3$ from above; whether the bound holds for every graph remains open.