On the equitable vertex arboricity of complete tripartite graphs

Abstract

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)-tree-coloring, which can be viewed as a generalization of proper equitable t-coloring. The strong equitable vertex k-arboricity of complete bipartite equipartition graphs was investigated in 2013. In this paper, we study the exact value of the strong equitable vertex 3-arboricity of complete equipartition tripartite graphs.