Forest maximum-degree repetition conjecture

Let $F$ be a forest on $n$ vertices, and let $f(F)=f_2(F)$ denote the minimum number of vertices that must be deleted to obtain an induced subgraph with at least two vertices attaining its maximum degree, or with fewer than two vertices. Forest conjecture. If

$$n\leq\frac{t^3+6t^2+17t+12}{6},$$

then $f(F)\leq t$, and this bound is sharp. This conjecture concerns the extremal value of the deletion parameter for forests; the supplied text does not establish it, so its resolution remains open.