The Tree Unimodality Conjecture

Let $T$ be a tree, let $\alpha=\alpha(T)$ be its independence number, and let $a_i$ denote the number of independent sets of cardinality $i$, so that $a_0=1$. The Tree Unimodality Conjecture. There exists an index $m$ such that

$$a_0\leq a_1\leq\cdots\leq a_m\geq a_{m+1}\geq\cdots\geq a_\alpha.$$

This conjecture asserts unimodality for independence sequences of trees, a family for which unimodality remains a central question despite counterexamples for general graphs. The supplied text does not state whether it has been resolved.