Chang–Roussel's upper-bound conjecture for power domination in uniform hypergraphs

Let $\mathcal{H}$ be a connected $r$-uniform hypergraph on $n$ vertices, and let $\gamma_p^k(\mathcal{H})$ denote its $k$-power domination number. Assume $k+r\leq n$. Chang–Roussel's conjecture. One has

$$\gamma_p^k(\mathcal{H}) \leq \frac{n}{r+k},$$

with equality if and only if $\mathcal{H}$ is a squid hypergraph of a connected $r$-uniform hypergraph, or $r=2$ and $\mathcal{H}=K_{k+2,k+2}$. The bound is known for $r\leq 4$, but the equality characterization, and indeed the conjecture itself, fails for $r\geq 7$, as the paper gives counterexamples.