The weighted subcubic triangle-free maximum-cut conjecture

Let $G$ be a weighted triangle-free graph with maximum degree at most $3$; equivalently, $G$ is a weighted triangle-free subcubic graph. Weighted subcubic conjecture. One should have

$$\operatorname{mac}(G)\geq \frac{4}{5}w(G).$$

This would extend the known unweighted Bondy–Locke result to edge-weighted graphs. The paper presents the assertion as open.