A conjecture on equitable vertex arboricity of graphs

Abstract

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