Gonality and edge subdivisions
From Egres Open
How does gonality change if each edge of the graph is subdivided [math]k[/math] times? 
- 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 . 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].
- ↑ 1.0 1.1 Josse van Dobben de Bruyn, Harry Smit, Marieke van der Wegen, Discrete and metric divisorial gonality can be different (2021) ArXiv Link