#### 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
##### 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 $12$ 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.

##### Keywords
tropical curves, prism graphs, lattice polygons, lattice point visibility
##### Mathematical Subject Classification
Primary: 14T15, 52C05