On gonality-tight graphs
Combinatorics
2025-11-25 v1 Algebraic Geometry
Abstract
We address a question posed by Fessler-Jensen-Kelsey-Owen regarding graphs whose second gonality is greater than the first by exactly 1. We answer the question affirmatively under a stronger condition, thereby characterising the entire gonality sequence for a large family of graphs. We prove a structure theorem for the graphs satisfying the condition, and show that they are all obtained via an inductive process by gluing together complete and banana graphs under certain rules.
Keywords
Cite
@article{arxiv.2511.19138,
title = {On gonality-tight graphs},
author = {Šimun Dropuljić and Yoav Len},
journal= {arXiv preprint arXiv:2511.19138},
year = {2025}
}
Comments
36 pages, 10 figures