Geodesic
Graphs of gonality three
Aidun, Ivan1 ; Dean, Frances2 ; Morrison, Ralph2 ; Yu, Teresa3 ; Yuan, Julie4
1 Oberlin College Department of Mathematics 10 N. Professor St. Oberlin OH 44074, USA
2 Williams College Department of mathematics and statistics 33 Stetson Ct. Williamstown MA 01267, USA
3 Williams College Department of mathematics and statistics 33 Stetson Ct. Williamstown MA 01267 USA
4 University of Minnesota-Twin Cities School of mathematics 206 Church St SE Minneapolis MN 55455, USA
Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1197-1217.

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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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DOI : 10.5802/alco.80
Classification : 14T05, 05C05, 05C57
Keywords: graph gonality, chip-firing, tropical geometry

Aidun, Ivan 1 ; Dean, Frances 2 ; Morrison, Ralph 2 ; Yu, Teresa 3 ; Yuan, Julie 4

1 Oberlin College Department of Mathematics 10 N. Professor St. Oberlin OH 44074, USA
2 Williams College Department of mathematics and statistics 33 Stetson Ct. Williamstown MA 01267, USA
3 Williams College Department of mathematics and statistics 33 Stetson Ct. Williamstown MA 01267 USA
4 University of Minnesota-Twin Cities School of mathematics 206 Church St SE Minneapolis MN 55455, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Aidun, Ivan; Dean, Frances; Morrison, Ralph; Yu, Teresa; Yuan, Julie. Graphs of gonality three. Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1197-1217. doi : 10.5802/alco.80. http://geodesic.mathdoc.fr/articles/10.5802/alco.80/

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