Alvarado et al.'s conjecture on minimum dominating sets in trees

Let $T$ be a tree with domination number $\gamma$, and let the number of its minimum dominating sets be measured as a function of $\gamma$. Alvarado et al.'s conjecture. A tree with domination number $\gamma$ has $O(\frac{\gamma2^\gamma}{\lngamma})$ minimum dominating sets. The conjecture was disproved by the explicit construction in this paper, which gives trees with more than $\frac{2}{5}\sqrt{5}^{\gamma}$ minimum dominating sets; thus the claimed asymptotic upper bound is false.