English

A simple and elementary proof of Whitney's unique embedding theorem

Combinatorics 2020-06-04 v2

Abstract

In this note we give a short and elementary proof of a more general version of Whitney's theorem that 3-connected planar graphs have a unique embedding in the plane. A consequence of the theorem is that cubic plane graphs cannot be embedded in a higher genus with a simple dual. The aim of this paper is to promote a simple and elementary proof, which is especially well suited for lectures presenting Whitney's theorem.

Keywords

Cite

@article{arxiv.2005.04895,
  title  = {A simple and elementary proof of Whitney's unique embedding theorem},
  author = {Gunnar Brinkmann},
  journal= {arXiv preprint arXiv:2005.04895},
  year   = {2020}
}
R2 v1 2026-06-23T15:26:48.790Z