Akiyama's linear arboricity conjecture

For a graph $G$, a linear forest is a forest whose components are paths, and the linear arboricity $la(G)$ is the minimum number of disjoint linear forests whose union contains all edges of $G$. Let $\Delta$ be the maximum degree of $G$.

Akiyama's linear arboricity conjecture. For every graph $G$ of maximum degree $\Delta$,

$$la(G)\leq \left\lceil\frac{\Delta+1}{2}\right\rceil.$$

The conjecture was raised by Akiyama and collaborators and is presented in the paper as a central related problem. The supplied text gives no resolution status.