  A $(q,r)$\emph{-tree-coloring} of a graph $G$ is a $q$-coloring of vertices
of $G$ such that the subgraph induced by each color class is a forest of
maximum degree at most $r.$ An \emph{equitable $(q, r)$-tree-coloring} of a
graph $G$ is a $(q,r)$-tree-coloring such that the sizes of any two color
classes differ by at most one. Let the \emph{strong equitable vertex
$r$-arboricity} be the minimum $p$ such that $G$ has an equitable $(q,
r)$-tree-coloring for every $q\geq p.$
  In this paper, we find the exact value for each $va^\equiv_2(K_{m,n})$ and
$va^\equiv_2(K_{l,m,n}).$
