Graphs of gonality three
Ivan Aidun, Frances Dean, Ralph Morrison, Teresa Yu, Julie Yuan

TL;DR
This paper extends the classification of hyperelliptic graphs to those with divisorial gonality three, providing new constructions and criteria for identifying such graphs under connectivity assumptions.
Contribution
It generalizes Chan's classification to a broader class of graphs with gonality three, including new construction methods and non-gonality conditions.
Findings
Classification extends to gonality three graphs under connectivity assumptions
Provides a construction method for graphs with gonality three
Offers criteria to determine when a graph is not of gonality three
Abstract
In 2013, Chan classified all metric hyperelliptic graphs, proving that divisorial gonality and geometric gonality are equivalent in the hyperelliptic case. We show that such a classification extends to combinatorial graphs of divisorial gonality three, under certain edge- and vertex-connectivity assumptions. We also give a construction for graphs of divisorial gonality three, and provide conditions for determining when a graph is not of divisorial gonality three.
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Taxonomy
TopicsAdvanced Graph Theory Research · Algebraic Geometry and Number Theory · Graph theory and applications
