English

A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings

Combinatorics 2020-11-20 v2

Abstract

We prove that for any parameter r an r-locally 2-connected graph G embeds r-locally planarly in a surface if and only if a certain matroid associated to the graph G is co-graphic. This extends Whitney's abstract planar duality theorem from 1932.

Keywords

Cite

@article{arxiv.2008.03027,
  title  = {A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings},
  author = {Johannes Carmesin},
  journal= {arXiv preprint arXiv:2008.03027},
  year   = {2020}
}
R2 v1 2026-06-23T17:41:58.180Z