The clasical Bers' theorem about pants decomposition says that any compact Riemann surface of genus $g \geq 2$ has a pants decomposition such that every cutting geodesic in this decomposition is of length $\leq \mathcal{B}_g$, where $\mathcal{B}_g$ is a constant (so-called Bers' constant) depending only on $g$. There are also estimations on Bers' constant.

My question is : What is known about Bers' constant on hyperbolic surfaces with boundary?

Thank you for your answers!