Buser's asymptotic conjecture for Bers' constants

Let $g$ and $n$ denote the genus and number of cusps of a hyperbolic surface, respectively. Its Bers' constant is the smallest number such that the surface admits a pants decomposition whose every curve has length at most that number. Buser's conjecture. Bers' constants for surfaces of genus $g$ with $n$ cusps behave roughly like $\sqrt{g+n}$. The conjecture concerns the asymptotic growth of Bers' constants as the topology varies. Existing upper bounds grow linearly in genus for closed surfaces and in Euler characteristic for surfaces with cusps, while known lower bounds grow like the square root of the Euler characteristic; the precise asymptotic behavior remains open.