A tropical version of Martens' theorem for metric graphs
Abstract
Abstract We study the conjecture stated by Jensen and Len on a tropical version on Martens' theorem via the Brill–Noether rank of a tropical curve. We recall Coppens' counterexample of Martens‐special chain of cycles, and we generalize the construction defining another class of graphs, Martens‐special trees of cycles, for which the conjecture does not hold in a similar setting. These are not the only counterexamples. However, we prove that the conjecture holds for all metric graphs with a stricter assumption on the degree in the Brill–Noether rank.
Fields of Study & Subjects
Polynomial and algebraic computation
Commutative Algebra and Its Applications
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 10
- Publication date
- 17 September 2026
- Language
- EN