Complex Analysis and Existence Problems for plane Graphs
Combinatorics
2026-07-27 v1 Algebraic Geometry
Complex Variables
Geometric Topology
Abstract
We show that a variety of known and new results concerning connected plane graphs whose vertex and face degrees satisfy prescribed uniformity conditions with at most two exceptions can be deduced from recent results on the Hurwitz existence problem regarding the realizability of branch patterns of rational functions. Our method also yields a description of the Belyi functions corresponding to such graphs.
Cite
@article{arxiv.2607.24061,
title = {Complex Analysis and Existence Problems for plane Graphs},
author = {Fedor Pakovich},
journal= {arXiv preprint arXiv:2607.24061},
year = {2026}
}