Hamid's independent transversal domination bound for connected graphs

Let $G$ be a non-complete connected graph on $n$ vertices. For a graph $G$, an independent transversal dominating set is a dominating set $S\subseteq V(G)$ such that $S\cap I\neq\emptyset$ for every maximum independent set $I\in\Omega(G)$; let $\gamma_{it}(G)$ denote the minimum cardinality of such a set. Hamid's conjecture.

$$\gamma_{it}(G)\leq\left\lceil\frac{n}{2}\right\rceil.$$

The preceding theorem establishes the bound when $\alpha(G)\geq n/2$; the paper states that this conjecture is not true in general.