Domination-packing conjecture for connected graphs

Let $G$ be a connected graph with at least two vertices. Write $\gamma(G)$ for its domination number, $\rho(G)$ for its packing number, and $\Delta$ for its maximum degree.

Domination-packing conjecture. For every such graph,

$$\gamma(G) \leq (\Delta-1)\rho(G)+1.$$

The paper presents this as a stronger version of the previously stated conjecture, following the known bound $\gamma(G)\leq\Delta\rho(G)$ for graphs without isolated vertices. The authors state that their techniques are still far from settling this conjecture.