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 [Formula: see text]-tree-coloring, which can be viewed as a generalization of proper equitable [Formula: see text]-coloring. The strong equitable vertex [Formula: see text]-arboricity of complete bipartite equipartition graphs was investigated in 2013. In this paper, we study the strong equitable vertex [Formula: see text]-arboricity of complete equipartition tripartite graphs. For most cases, the exact values of [Formula: see text] are obtained.