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An equitable (t,k)-tree-coloring of a graph G is a coloring of vertices of G such that the sizes of any two color classes differ by at most one and the subgraph induced by each color class is a forest of maximum degree at most k. The minimum t such that G has an equitable (t′,k)-tree-coloring for every t′≥t, denoted by vak≡(G), is the strong equitable vertex k-arboricity. In this paper, we give sharp...