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arXiv:2106.12568 [math.CO]AbstractReferencesReviewsResources

Discrete and metric divisorial gonality can be different

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

Published 2021-06-23Version 1

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.

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