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arXiv · 1908.04320

Tropically planar graphs

Desmond Coles·Neelav Dutta·Sifan Jiang·Ralph Morrison·Andrew Scharf
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Abstract

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.

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Desmond Coles, Neelav Dutta, Sifan Jiang, Ralph Morrison, Andrew Scharf. 2019-08-12. Tropically planar graphs. https://arxiv.org/abs/1908.04320

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