Abstract
There are several notions of gonality for graphs. The divisorial gonality dgon(G) of a graph G is the smallest degree of a divisor of positive rank in the sense of Baker-Norine. The stable gonality sgon(G) of a graph G is the minimum degree of a finite harmonic morphism from a refinement of G to a tree, as defined by Cornelissen, Kato and Kool. We show that computing dgon(G) and sgon(G) are NP-hard by a reduction from the maximum independent set problem and the vertex cover problem, respectively. Both constructions show that computing gonality is moreover APX-hard.
Original language | English |
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Pages (from-to) | 134-149 |
Number of pages | 16 |
Journal | Discrete Applied Mathematics |
Volume | 287 |
DOIs | |
Publication status | Published - 2020 |
Keywords
- Gonality
- Computational complexity
- Chip-firing
- Graph theory
- Tropical geometry