The equitable vertex arboricity of complete tripartite graphs

•Equitable vertex arboricity has strong applications such as scheduling.•Generalize the equitable vertex 1-arboricity of complete bipartite graphs.•Most of the exact values of equitable vertex 2-arboricity of Kn,n,nKn,n,n are determined.

The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu et al. introduced the concept of equitable (t,k)(t,k)-tree-coloring, which can be viewed as a generalization of proper equitable t-coloring. Wu et al. investigated the strong equitable vertex k-arboricity of complete bipartite graphs. In this paper, we mainly investigate the strong equitable vertex 2-arboricity of complete tripartite graphs.