Planarity and duality of finite and infinite graphs

@article{Thomassen1980PlanarityAD,
  title={Planarity and duality of finite and infinite graphs},
  author={Carsten Thomassen},
  journal={J. Comb. Theory, Ser. B},
  year={1980},
  volume={29},
  pages={244-271}
}
We present a short proof of the following theorems simultaneously: Kuratowski’s theorem, Fary’s theorem, and the theorem of Tutte that every 3-connected planar graph has a convex representation. We stress the importance of Kuratowski’s theorem by showing how it implies a result of Tutte on planar representations with prescribed vertices on the same facial cycle as well as the planarity criteria of Whitney, MacLane, Tutte, and Fournier (in the case of Whitney’s theorem and MacLane’s theorem this… CONTINUE READING
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