The separating systole and the genus ratio of high genus triangulations

We show that the separating systole of high genus triangulations is of logarithmic order (in the size of the triangulation). Our methods also allow us to show an enumerative result, i.e. the convergence of the “genus ratio” for high genus triangulations. This complements the convergence of the “size ratio” that was proven in previous work with Budzinski.