Fractional Akiyama–Watanabe conjecture for triangle-free planar graphs

Let $G$ be a triangle-free planar graph, and let $\fva(G)$ denote its fractional vertex-arboricity. Fractional Akiyama–Watanabe conjecture. Every triangle-free planar graph has fractional vertex-arboricity at most $8/5$, that is,

$$\fva(G)\leq \frac{8}{5}.$$

This generalizes the Akiyama–Watanabe conjecture from bipartite planar graphs to the weaker triangle-free condition. The corresponding induced-forest conjecture remains open; the paper records the best known partial bounds and proposes this fractional strengthening.