Divisorial Gonality of Banana Trees in Quadratic Time
Manuscript 19 October 2026 · Online 19 October 2026
Abstract
A banana tree is a connected loopless multigraph whose underlying simple graph is a tree. We give an exact algorithm that computes its divisorial gonality and an effective divisor attaining it in O(n^2) word operations and O(n^2) space after reading the input, where n is the number of vertices. Multiplicities may be supplied in binary. A rooted residue normal form reduces positive rank to positivity of one pile at every root. A dynamic program combines independent child costs conditional on the parent pile, and sliding-window minima evaluate the recurrence in quadratic time. The result covers arbitrary branching, extending the cubic path algorithm of Beougher et al. The gonality conjecture for banana trees was already proved in that work; this paper does not resolve the general multigraph conjecture. The proof is self-audited, AI-assisted and unrefereed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete banana-tree algorithm
- Categories
- math.CO · cs.DS
- Manuscript
- 19 October 2026
- Online release
- 19 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Divisorial Gonality of Banana Trees in Quadratic Time,” EulerSolve Research Papers, AMR-029-0087, 2026. https://doi.org/10.5281/zenodo.23467234.
BibTeX
@misc{ferudun2026bananatreegonality,
author = {Ferudun, Alper},
title = {Divisorial Gonality of Banana Trees in Quadratic Time},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/amr-029-0087/},
doi = {10.5281/zenodo.23467234},
note = {AMR-029-0087; unrefereed preprint}
}