Faudree et al.'s subcubic strong edge coloring conjectures

Let $G$ be a subcubic graph, meaning a graph with maximum degree at most three. Let $\chiup_{s}'(G)$ denote its strong chromatic index.

Faudree et al.'s subcubic conjectures. \begin{enumerate} \item The strong chromatic index is at most $10$. \item If $G$ is bipartite, then $\chiup_{s}'(G) \leq 9$. \item If $G$ is planar, then $\chiup_{s}'(G) \leq 9$. \item If $G$ is bipartite and the degree sum of every edge is at most $5$, then $\chiup_{s}'(G) \leq 6$. \item If $G$ is bipartite with girth at least $6$, then $\chiup_{s}'(G) \leq 7$. \item If $G$ is bipartite and its girth is large, then $\chiup_{s}'(G) \leq 5$. \end{enumerate}

The first assertion was independently confirmed by Andersen and by Horák et al., and agrees with the Erdős–Nešetřil bound when $\Delta=3$. The source gives no resolution status for the remaining assertions.