The decycling number \(\nabla (G)\) of a graph G is the minimum number of vertices that must be removed to eliminate all cycles in G. The forest number f(G) is the maximum number of vertices that induce a forest in G. So \(\nabla (G) + f(G) = |V(G)|\) . For the Cartesian product \(T \,\square \, T'\) of trees T and \(T'\) it is proved that \(\nabla (S_n \,\square \, S_{n'}) \le \nabla (T \,\square \, T')\) , thus resolving the conjecture of Wang and Wu asserting that \(f(T \,\square \, T') \le f(S_n \,\square \, S_{n'})\) . It is shown that \(\nabla (T \,\square \, T') \ge \min \{ |V(T)|,|V(T')|\} - 1\) and the equality cases characterized. For prisms over trees, it is proved that \(\nabla (T\,\square \, K_2) = \alpha '(T)\) , and for arbitrary graphs \(G_1\) and \(G_2\) , it is proved that \(\nabla (G_1 \,\square \, G_2) \ge \alpha '(G_1) \alpha '(G_2)\) , where \(\alpha '\) is the matching number.
