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 \(\Delta (G)\) is the maximum degree of G and m is an integer with \(m\ge \lceil \frac{\Delta (G)+1}{2}\rceil \). This conjecture is verified for 5-degenerate graphs in this paper.
['Guantao Chen', 'Yuping Gao', 'Songling Shan', 'Guanghui Wang', 'Jian-Liang Wu']
Equitable vertex arboricity of 5-degenerate graphs