A conjecture on equitable vertex arboricity of graphs

Wu, Zhang and Li [4] conjectured that the set of vertices of any simple graph $G$ can be equitably partitioned into $\lceil (\mathrm{\Delta }(G)+1)\mathrm{/}2\rceil$ subsets so that each of them induces a forest of $G$. In this note, we prove this conjecture for graphs $G$ with $\mathrm{\Delta }(G)\ge \mathrm{\mid }G\mathrm{\mid }\mathrm{/}2$.