Discrete and metric divisorial gonality can be different

Journal article (2022)

Authors

J. van Dobben de Bruyn Discrete Mathematics and Optimization - EEMCS
Harry Smit Max Planck Institute for Mathematics
Marieke van der Wegen Universiteit Utrecht
Research Group
Discrete Mathematics and Optimization (EEMCS) (TU Delft)
Copyright: © 2022 J. van Dobben de Bruyn, Harry Smit, Marieke van der Wegen
DOI: https://doi.org/10.1016/j.jcta.2022.105619
Finite graph Metric graph Gonality Chip-firing game
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Discrete Mathematics and Optimization

Abstract

This paper compares the divisorial gonality of a finite graph G to the divisorial gonality of the associated metric graph Γ(G,1) with unit lengths. We show that dgon(Γ(G,1)) is equal to the minimal divisorial gonality of all regular subdivisions of G, and we provide a class of graphs for which this number is strictly smaller than the divisorial gonality of G. This settles a conjecture of M. Baker [3, Conjecture 3.14] in the negative.