An equitable partition of a graph is a partition of the vertex-set of such that the sizes of any two parts differ by at most one. We show that every graph with an acyclic coloring with at most colors can be equitably partitioned into induced forests. We also prove that for any integers and , any -degenerate graph can be equitably partitioned into induced forests.
Each of these results implies the existence of a constant such that for any , any planar graph has an equitable partition into induced forests. This was conjectured by Wu, Zhang, and Li in 2013.