Discrete and metric divisorial gonality can be different

Josse van Dobben de Bruyn; Harry Smit; Marieke van der Wegen

doi:10.1016/j.jcta.2022.105619

Discrete and metric divisorial gonality can be different

Josse van Dobben de Bruyn^*, Harry Smit, Marieke van der Wegen

^*Corresponding author for this work

Discrete Mathematics and Optimization

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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.

Original language	English
Article number	105619
Pages (from-to)	1-19
Number of pages	19
Journal	Journal of Combinatorial Theory. Series A
Volume	189
DOIs	https://doi.org/10.1016/j.jcta.2022.105619
Publication status	Published - 2022

Funding

Dutch Research Council (NWO), project number 613.009.127.

Keywords

Chip-firing game
Finite graph
Gonality
Metric graph

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10.1016/j.jcta.2022.105619

1-s2.0-S0097316522000279-mainFinal published version, 465 KBLicence: CC BY

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AB - 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.

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Discrete and metric divisorial gonality can be different

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