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Drawing Planar Graphs with Prescribed Face Areas

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Graph-Theoretic Concepts in Computer Science (WG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9941))

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Abstract

We study drawings of planar graphs such that every inner face has a prescribed area. A plane graph is area-universal if for every area assignment on the inner faces, there exists a straight-line drawing realizing the assigned areas. It is known that not all plane graphs are area-universal. The only counterexample in literature is the octahedron graph.

We give a counting argument that allows to prove non-area-universality for a large class of triangulations. Moreover, we relax the straight-line property of the drawings, namely we allow the edges to bend. We show that one bend per edge is enough to realize any face area assignment of every plane graph. For plane bipartite graphs, it suffices that half of the edges have a bend.

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Acknowledgments

We thank Stefan Felsner und Udo Hoffmann for discussions about the problem and helpful comments on drafts of this manuscript.

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Authors and Affiliations

  1. Institut für Mathematik, TU Berlin, Berlin, Germany

    Linda Kleist

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  1. Linda Kleist
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Correspondence to Linda Kleist .

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Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Pinar Heggernes

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Kleist, L. (2016). Drawing Planar Graphs with Prescribed Face Areas. In: Heggernes, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2016. Lecture Notes in Computer Science(), vol 9941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53536-3_14

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  • DOI: https://doi.org/10.1007/978-3-662-53536-3_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53535-6

  • Online ISBN: 978-3-662-53536-3

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