Wang–Wu's forest-number conjecture for Cartesian products of trees

Let $T$ and $T'$ be trees of respective orders $n$ and $n'$. For each graph $G$, let $f(G)$ denote the maximum number of vertices that induce a forest in $G$, and let $S_n$ denote the star on $n$ vertices.

Wang–Wu's conjecture.

$$f(T \operatorname{\,\square\,} T') \leq f(S_n \operatorname{\,\square\,} S_{n'}).$$

This conjecture was resolved by the paper: the authors prove the equivalent decycling-number inequality in the opposite direction, using $\nabla(G)+f(G)=|V(G)|$ for Cartesian products with the same order. The extremal role of the product of stars is therefore established.