On minimal generating sets for the mapping class group of a punctured surface

Let Σ_g,p be an oriented surface of genus g with p punctures. We denote by \(\cal{M}_{g,p}\) $${\mathcal{M}}_{g,p}$$ and \(\cal{M}_{g,p}^{\pm}\) $${\mathcal{M}}_{g,p}^{\pm }$$ the mapping class group and the extended mapping class group of Σ_g,p, respectively. In this paper, we show that \(\cal{M}_{g,p}\) $${\mathcal{M}}_{g,p}$$ and \(\cal{M}_{g,p}^{\pm}\) $${\mathcal{M}}_{g,p}^{\pm }$$ are generated by two elements for g ≥ 3 and p ≥ 0.