  Let $S_{0,n}$ be an $n$-punctured sphere. For $n\geq 4$, we construct a
sequence $(\mathcal{X}_i)_{i\in\mathbb{N}}$ of finite rigid sets in the pants
graph $\mathcal{P}(S_{0,n})$ such that $\mathcal{X}_1 \subset \mathcal{X}_2
\subset ...\subset\mathcal{P}(S_{0,n})$ and
$\bigcup_{i\geq1}\mathcal{X}_i=\mathcal{P}(S_{0,n})$.
