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Abstract
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
1 2 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
1 1 . 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.
Keywords
tropical curves, prism graphs, lattice polygons, lattice
point visibility
Mathematical Subject Classification
Primary: 14T15, 52C05
Milestones
Received: 9 October 2020
Revised: 8 January 2021
Accepted: 23 January 2021
Published: 17 July 2021
Communicated by Kenneth S. Berenhaut