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

Gunnar Brinkmann

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 also 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


Polyhedra, graph, embedding

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DOI: https://doi.org/10.26493/1855-3974.2334.331

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications