Discrete and metric divisorial gonality can be different

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

doi:10.1016/j.jcta.2022.105619

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Journal Article

Discrete and metric divisorial gonality can be different

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Smit, Harry
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1016/j.jcta.2022.105619
(Publisher version)

https://doi.org/10.48550/arXiv.2106.12568
(Preprint)

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vanDobbendeBruyn-Smit-vanderWegen_Discrete and metric divisorial gonality can be different_2022.pdf
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Citation

de Bruyn, J. v. D., Smit, H., & van der Wegen, M. (2022). Discrete and metric divisorial gonality can be different. Journal of Combinatorial Theory, Series A, 189: 105619. doi:10.1016/j.jcta.2022.105619.

Cite as: https://hdl.handle.net/21.11116/0000-000A-53A2-1

Abstract

This paper compares the divisorial gonality of a finite graph $G$ to the
divisorial gonality of the associated metric graph $\Gamma(G,\mathbb{1})$ with
unit lengths. We show that $\text{dgon}(\Gamma(G,\mathbb{1}))$ 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 in the negative.