Abstract
The rth gonality of a graph is the smallest degree of a divisor on the graph with rank r. The gonality sequence of a graph is a tropical analogue of the gonality sequence of an algebraic curve. We show that the set of truncated gonality sequences of graphs forms a semigroup under addition. Using this, we study which triples (x, y, z) can be the first three terms of a graph gonality sequence. We show that nearly every such triple with (Formula present) is the first three terms of a graph gonality sequence, and also exhibit triples where the ratio (Formula present) is an arbitrary rational number between 1 and 3. In the final section, we study algebraic curves whose rth and (r + 1) st gonality differ by 1, and posit several questions about graphs with this property.
Original language | English |
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Pages (from-to) | 343-361 |
Number of pages | 19 |
Journal | Australasian Journal of Combinatorics |
Volume | 88 |
Issue number | 3 |
State | Published - 2024 |
Bibliographical note
Publisher Copyright:© The author(s).
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics