# Gonality and edge subdivisions

From Egres Open

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

## Remarks

- 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].

### References

- ↑
^{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