Dorbec et al.'s power domination bound for connected regular graphs

Let $G$ be a connected $r$-regular graph of order $n$, with $r\ge 3$, and let $k\ge 1$. Write $\gamma_{p,k}(G)$ for the minimum cardinality of a $k$-power dominating set of $G$. Assume that $G\not\cong K_{r,r}$. Dorbec et al.'s conjecture. Then

$$\gamma_{p,k}(G)\le \frac{n}{r+1}.$$

This conjecture extends known upper bounds for $k$-power domination in regular graphs by removing the claw-free hypothesis. Its status is unclear from the supplied text.