Tropically planar graphs

Coles, Desmond ^[2] ; Dutta, Neelav ^[1] ; Jiang, Sifan ^[3] ; Morrison, Ralph ^[4] ; Scharf, Andrew ^[4]
1. [1] University of Virginia
  
  University of Virginia
  
  Estados Unidos
2. [2] Department of Mathematics, UT Austin, 2515 Speedway, RLM 8.100, Austin, TX, 78712, USA
3. [3] International and Development Economics, Yale University, P.O. Box 208269, New Haven, CT, 06520-8269, USA
4. [4] Department of Mathematics and Statistics, Williams College, 33 Stetson Ct., Williamstown, MA, 01267, USA
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Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 27-60
Idioma: inglés
DOI: 10.1007/s13348-021-00335-4
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Resumen
- We study tropically planar graphs, which are the graphs that appear in smooth tropical plane curves. We develop necessary conditions for graphs to be tropically planar, and compute the number of tropically planar graphs up to genus 7. We provide non-trivial upper and lower bounds on the number of tropically planar graphs, and prove that asymptotically 0% of connected trivalent planar graphs are tropically planar.