Vol. 14, No. 3, 2021

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Prism graphs in tropical plane curves

Liza Jacoby, Ralph Morrison and Ben Weber

Vol. 14 (2021), No. 3, 495–510

Any smooth tropical plane curve contains a distinguished trivalent graph called its skeleton. In 2020 Morrison and Tewari proved that the so-called big-face graphs cannot be the skeleta of tropical curves for genus 12 and greater. In this paper we answer an open question they posed to extend their result to the prism graphs, proving that a prism graph is the skeleton of a smooth tropical plane curve precisely when the genus is at most 11. Our main tool is a classification of lattice polygons with two points that can simultaneously view all others, without having any one point that can observe all others.

tropical curves, prism graphs, lattice polygons, lattice point visibility
Mathematical Subject Classification
Primary: 14T15, 52C05
Received: 9 October 2020
Revised: 8 January 2021
Accepted: 23 January 2021
Published: 17 July 2021

Communicated by Kenneth S. Berenhaut
Liza Jacoby
Wiliams College
Williamstown, MA
United States
Ralph Morrison
Williams College
Williamstown, MA
United States
Ben Weber
Williams College
Williamstown, MA
United States