Equitable induced-forest partition conjecture for bounded-degree graphs

Let $G$ be a graph with maximum degree $\Delta$. An equitable partition is a partition of the vertex set into parts whose sizes differ by at most one, and an induced forest is a vertex-induced subgraph that is a forest. Equitable induced-forest partition conjecture. For any integers $\Delta$ and $k\geqslant\left\lceil\frac{\Delta+1}{2}\right\rceil$, every graph of maximum degree $\Delta$ can be equitably partitioned into $k$ induced forests. The provided excerpt does not state whether this conjecture has been resolved, so its status remains open here.