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

Delft University of Technology

Research output: Contribution to journal › Article › Academic › peer-review

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
Journal	Journal of Combinatorial Theory. Series A
Volume	189
DOIs	https://doi.org/10.1016/j.jcta.2022.105619
Publication status	Published - Jul 2022

Bibliographical note

Funding Information:
We are grateful to Dion Gijswijt, Sophie Huiberts and Alejandro Vargas for helpful discussions. The first author is partially supported by the Dutch Research Council (NWO), project number 613.009.127 . The second author would like to thank the Max Planck Institute for Mathematics Bonn for its financial support.

Publisher Copyright:
© 2022 The Author(s)

Funding

We are grateful to Dion Gijswijt, Sophie Huiberts and Alejandro Vargas for helpful discussions. The first author is partially supported by the Dutch Research Council (NWO), project number 613.009.127 . The second author would like to thank the Max Planck Institute for Mathematics Bonn for its financial support.

Keywords

Chip-firing game
Finite graph
Gonality
Metric graph

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10.1016/j.jcta.2022.105619Licence: CC BY

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

Cite this

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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.",

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AU - van der Wegen, Marieke

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KW - Chip-firing game

KW - Finite graph

KW - Gonality

KW - Metric graph

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Discrete and metric divisorial gonality can be different

Abstract

Bibliographical note

Funding

Keywords

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