The $m(G)/17$ bound for induced matchings without $C_5^2$ components

Let $G$ be a graph, let $m(G)$ denote its number of edges, and let $C_5^2$ denote the graph obtained by replacing each vertex of a $5$-cycle with an independent set of order $2$. An induced matching is a matching whose endpoints induce exactly the edges in the matching; write $u_s(G)$ for the maximum size of an induced matching in $G$. The $m(G)/17$ conjecture. If $G$ has maximum degree at most $4$ and no component is isomorphic to $C_5^2$, then

$$\nu_s(G)\geq \frac{m(G)}{17}.$$

The preceding theorem gives the best possible general bound with a possible $C_5^2$ component, while the source notes that no example without such a component attaining the weaker ratio $m(G)/18$ was known. The proposed bound remains open in the paper.