Stable Divisorial Gonality is in NP

Hans L. Bodlaender, Marieke van der Wegen*, Tom C. van der Zanden

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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 et al., we obtain that stable divisorial gonality is NP-complete. The proof consists of a partial certificate that can be verified by solving an Integer Linear Programming instance. As a corollary, we have that the total number of subdivisions needed for minimum stable divisorial gonality of a graph with m edges is bounded by mO(mn).
Original languageEnglish
Number of pages13
JournalTheory of Computing Systems
Publication statusE-pub ahead of print - 7 Dec 2020


  • Computational complexity
  • Graphs
  • Gonality

Cite this