Strong equitable vertex arboricity bounded by maximum degree

Let $G$ be a graph, let $\Delta(G)$ denote its maximum degree, and let $a^*_{eq}(G)$ be the smallest integer $t$ such that $G$ has an equitable $t'$-tree-coloring for every $t'\geq t$, where an equitable $k$-tree-coloring is a partition of $V(G)$ into $k$ parts whose sizes differ by at most one and each part induces a forest. Strong equitable vertex arboricity conjecture.

$$a^*_{eq}(G)\leq \left\lceil\frac{\Delta(G)+1}{2}\right\rceil$$

This conjecture proposes a maximum-degree bound for the strong equitable vertex arboricity of every graph. Its resolution is not specified in the source.