  For an orientable surface $S$ of finite topological type with genus $g \geq
3$, we construct a finite set of curves whose union of iterated rigid
expansions is the curve graph of $S$. The set constructed, and the method of
rigid expansion, are closely related to Aramayona and Leiniger's finite rigid
set, and in fact a consequence of our proof is that Aramayona and Leininger's
set also exhausts the curve graph via rigid expansions.
