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Upward Straight-Line Embeddings of Directed Graphs into Point Sets

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Graph-Theoretic Concepts in Computer Science (WG 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5344))

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Abstract

In this paper we consider the problem of characterizing the directed graphs that admit an upward straight-line embedding into every point set in convex or in general position. In particular, we show that no biconnected directed graph admits an upward straight-line embedding into every point set in convex position, and we provide a characterization of the Hamiltonian directed graphs that admit upward straight-line embeddings into every point set in general or in convex position. We also describe how to construct upward straight-line embeddings of directed paths into convex point sets and we prove that for directed trees such embeddings do not always exist. Further, we investigate the related problem of upward simultaneous embedding without mapping, proving that deciding whether two directed graphs admit an upward simultaneous embedding without mapping is \(\cal NP\)-hard.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Arizona, U.S.A.

    Alejandro Estrella-Balderrama & Stephen G. Kobourov

  2. Dipartimento di Informatica e Automazione, Università di Roma Tre, Italy

    Fabrizio Frati

Authors
  1. Alejandro Estrella-Balderrama
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  2. Fabrizio Frati
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  3. Stephen G. Kobourov
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Durham University, South Road, DH1 3LE, Durham, UK

    Hajo Broersma , Tom Friedetzky  & Daniel Paulusma ,  & 

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2008 Springer-Verlag Berlin Heidelberg

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Estrella-Balderrama, A., Frati, F., Kobourov, S.G. (2008). Upward Straight-Line Embeddings of Directed Graphs into Point Sets. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2008. Lecture Notes in Computer Science, vol 5344. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92248-3_12

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  • DOI: https://doi.org/10.1007/978-3-540-92248-3_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-92247-6

  • Online ISBN: 978-3-540-92248-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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