Gonality and edge subdivisions

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How does gonality change if each edge of the graph is subdivided [math]k[/math] times? [1]


  • van Dobben de Bruyn, Smit, and van der Wegen shows that the gonality can change upon subdivision: They show an infinite family of graphs where the subdivision of each edge by a vertex can decrease gonality [1]. However, they pose the question if the ratio of the gonalities can be bounded, or if the gonality can change upon subdividing each edge into [math]k[/math] segments for an odd [math]k[/math].


  1. 1.0 1.1 Josse van Dobben de Bruyn, Harry Smit, Marieke van der Wegen, Discrete and metric divisorial gonality can be different (2021) ArXiv Link