The girth-five frustration index conjecture for signed subcubic graphs

Let $(G,\sigma)$ be a signed connected simple subcubic graph, where $v(G)$ denotes the number of vertices of $G$, $F(G,\sigma)$ denotes its frustration index, and the girth is the length of its shortest cycle. Girth-five frustration index conjecture. If $(G,\sigma)$ has girth at least $5$, then

$$F(G,\sigma)\leq \frac{3}{10}v(G).$$

This proposes an improved upper bound for the frustration index when short cycles are forbidden; its status is open in the supplied source.