Garijo–González–Márquez conjecture on location-domination in twin-free connected graphs

Let $\lambda_{|\mathcal C^*}(n)$ denote the maximum location-domination number of a twin-free, connected graph on $n$ vertices. Garijo–González–Márquez conjecture. There exists a positive integer $n_1$ such that, for every $n\ge n_1$,

$$\lambda_{|\mathcal C^*}(n)=\left\lfloor\frac{n}{2}\right\rfloor.$$

Garijo, González, and Márquez proved the matching lower bound for every $n\ge14$; the conjecture asserts that this lower bound is eventually exact.