The disjoint domination number with a perfect matching is bounded by independence number

Let $G$ be a connected graph containing a swap set. Let $DD_{\operatorname{m}}(G)$ denote the minimum size of a disjoint dominating set whose two parts are joined by a perfect matching, and let $\alpha(G)$ be the independence number of $G$. Disjoint-domination independence conjecture.

$$DD_{\operatorname{m}}(G)\leq\alpha(G).$$

The conjecture asserts the existence of a desired matching between two disjoint dominating sets whose total size is controlled by the independence number. The supplied text does not state whether this conjecture has been resolved.