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Main Authors:	Dropuljić, Šimun, Len, Yoav
Format:	Preprint
Published:	2025
Subjects:	Combinatorics Algebraic Geometry 14H51, 05C57, 14T15
Online Access:	https://arxiv.org/abs/2511.19138
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author	Dropuljić, Šimun Len, Yoav
author_facet	Dropuljić, Šimun Len, Yoav
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2511_19138
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	On gonality-tight graphs Dropuljić, Šimun Len, Yoav Combinatorics Algebraic Geometry 14H51, 05C57, 14T15 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.
title	On gonality-tight graphs
topic	Combinatorics Algebraic Geometry 14H51, 05C57, 14T15
url	https://arxiv.org/abs/2511.19138

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