Tropically planar graphs
Algebraic Geometry
2020-02-06 v3 Combinatorics
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 . We provide non-trivial upper and lower bounds on the number of tropically planar graphs, and prove that asymptotically of connected trivalent planar graphs are tropically planar.
Keywords
Cite
@article{arxiv.1908.04320,
title = {Tropically planar graphs},
author = {Desmond Coles and Neelav Dutta and Sifan Jiang and Ralph Morrison and Andrew Scharf},
journal= {arXiv preprint arXiv:1908.04320},
year = {2020}
}
Comments
28 pages, 29 figures; updated to correct erroneous counts at the end of Section 3