Discrete and metric divisorial gonality can be different
Josse van Dobben de Bruyn (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Harry Smit (Max Planck Institute for Mathematics)
Marieke van der Wegen (Universiteit Utrecht)
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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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