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Geodesic Embeddings and Planar Graphs

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Abstract

Schnyder labelings are known to have close links to order dimension and drawings of planar graphs. It was observed by Ezra Miller that geodesic embeddings of planar graphs are another class of combinatorial or geometric objects closely linked to Schnyder labelings. We aim to contribute to a better understanding of the connections between these objects. In this article we prove

• a characterization of 3-connected planar graphs as those graphs admitting rigid geodesic embeddings,

• a bijection between Schnyder labelings and rigid geodesic embeddings,

• a strong version of the Brightwell–Trotter theorem.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Stefan Felsner

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  1. Stefan Felsner
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Felsner, S. Geodesic Embeddings and Planar Graphs. Order 20, 135–150 (2003). https://doi.org/10.1023/B:ORDE.0000009251.68514.8b

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  • DOI: https://doi.org/10.1023/B:ORDE.0000009251.68514.8b

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