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International Symposium on Graph Drawing

GD 2013: Graph Drawing pp 292–303Cite as

Drawing Non-Planar Graphs with Crossing-Free Subgraphs

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8242)

Abstract

We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing Γ of G in the plane such that the edges of S are not crossed in Γ? We give positive and negative results for different kinds of spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G ∖ S; in this setting different trade-offs between number of bends and drawing area are given.

Keywords

  • Span Tree
  • Planar Graph
  • Geometric Graph
  • Span Subgraph
  • Graph Drawing

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Work on these results began at the 8th Bertinoro Workshop on Graph drawing. Discussion with other participants is gratefully acknowledged. Part of the research was conducted in the framework of ESF project 10-EuroGIGA-OP-003 GraDR “Graph Drawings and Representations”.

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Author information

Authors and Affiliations

  1. Università Roma Tre, Italy

    Patrizio Angelini, Giordano Da Lozzo & Maurizio Patrignani

  2. Università degli Studi di Perugia, Italy

    Carla Binucci, Walter Didimo, Luca Grilli & Fabrizio Montecchiani

  3. Institute of Computer Science-FORTH, Univ. of Crete, Greece

    Ioannis G. Tollis

Authors
  1. Patrizio Angelini
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  2. Carla Binucci
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  3. Giordano Da Lozzo
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  4. Walter Didimo
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  5. Luca Grilli
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  6. Fabrizio Montecchiani
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  7. Maurizio Patrignani
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  8. Ioannis G. Tollis
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Dr., T1K-3M4, Lethbridge, AB, Canada

    Stephen Wismath

  2. Institut für Informatik, Universität Würzburg, Am Hubland, 97074, Würzburg, Germany

    Alexander Wolff

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Angelini, P. et al. (2013). Drawing Non-Planar Graphs with Crossing-Free Subgraphs. In: Wismath, S., Wolff, A. (eds) Graph Drawing. GD 2013. Lecture Notes in Computer Science, vol 8242. Springer, Cham. https://doi.org/10.1007/978-3-319-03841-4_26

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  • DOI: https://doi.org/10.1007/978-3-319-03841-4_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03840-7

  • Online ISBN: 978-3-319-03841-4

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