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:

Accepted:

Published online:

DOI: 10.5802/alco.80

Keywords: graph gonality, chip-firing, tropical geometry

^{1}; Dean, Frances

^{2}; Morrison, Ralph

^{2}; Yu, Teresa

^{3}; Yuan, Julie

^{4}

@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}, pages = {1197--1217}, publisher = {MathOA foundation}, volume = {2}, number = {6}, year = {2019}, doi = {10.5802/alco.80}, mrnumber = {4049843}, zbl = {07140430}, language = {en}, url = {http://www.numdam.org/articles/10.5802/alco.80/} }

TY - JOUR AU - Aidun, Ivan AU - Dean, Frances AU - Morrison, Ralph AU - Yu, Teresa AU - Yuan, Julie TI - Graphs of gonality three JO - Algebraic Combinatorics PY - 2019 SP - 1197 EP - 1217 VL - 2 IS - 6 PB - MathOA foundation UR - http://www.numdam.org/articles/10.5802/alco.80/ DO - 10.5802/alco.80 LA - en ID - ALCO_2019__2_6_1197_0 ER -

%0 Journal Article %A Aidun, Ivan %A Dean, Frances %A Morrison, Ralph %A Yu, Teresa %A Yuan, Julie %T Graphs of gonality three %J Algebraic Combinatorics %D 2019 %P 1197-1217 %V 2 %N 6 %I MathOA foundation %U http://www.numdam.org/articles/10.5802/alco.80/ %R 10.5802/alco.80 %G en %F 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. http://www.numdam.org/articles/10.5802/alco.80/

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