Equitable vertex arboricity of 5-degenerate graphs

Wu et al. (Discret Math 313:2696–2701, 2013) conjectured that the vertex set of any simple graph G can be equitably partitioned into m subsets so that each subset induces a forest, where $\mathrm{\Delta }(G)$ is the maximum degree of G and m is an integer with $m\ge \lceil \frac{\mathrm{\Delta }(G)+1}{2}\rceil$ . This conjecture is verified for 5‐degenerate graphs in this paper.