  Divisorial gonality and stable divisorial gonality are graph parameters,
which have an origin in algebraic geometry. Divisorial gonality of a connected
graph $G$ can be defined with help of a chip firing game on $G$. The stable
divisorial gonality of $G$ is the minimum divisorial gonality over all
subdivisions of edges of $G$.
  In this paper we prove that deciding whether a given connected graph has
stable divisorial gonality at most a given integer $k$ belongs to the class NP.
Combined with the result that (stable) divisorial gonality is NP-hard by
Gijswijt, we obtain that stable divisorial gonality is NP-complete. The proof
consist of a partial certificate that can be verified by solving an Integer
Linear Programming instance. As a corollary, we have that the number of
subdivisions needed for minimum stable divisorial gonality of a graph with $n$
vertices is bounded by $2^{p(n)}$ for a polynomial $p$.
