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.

Revised : 2019-03-31

Accepted : 2019-04-10

Published online : 2019-12-04

DOI : https://doi.org/10.5802/alco.80

Classification: 14T05, 05C05, 05C57

Keywords: graph gonality, chip-firing, tropical geometry

@article{ALCO_2019__2_6_1197_0, author = {Aidun, Ivan and Dean, Frances and Morrison, Ralph and Yu, Teresa and Yuan, Julie}, title = {Graphs of gonality three}, journal = {Algebraic Combinatorics}, publisher = {MathOA foundation}, volume = {2}, number = {6}, year = {2019}, pages = {1197-1217}, doi = {10.5802/alco.80}, language = {en}, url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1197_0} }

Aidun, Ivan; Dean, Frances; Morrison, Ralph; Yu, Teresa; Yuan, Julie. Graphs of gonality three. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1197-1217. doi : 10.5802/alco.80. https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1197_0/

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