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A Linear-Time Algorithm for Testing Outer-1-Planarity

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Abstract

A graph is 1-planar if it can be embedded in the plane with at most one crossing per edge. It is known that the problem of testing 1-planarity of a graph is NP-complete. In this paper, we study outer-1-planar graphs. A graph is outer-1-planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a given graph is outer-1-planar. The algorithm can be used to produce an outer-1-planar embedding in linear time if it exists.

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Acknowledgments

This research arose at the Port Douglas Workshop on Geometric Graph Theory, June, 2011, in Australia. The workshop was supported by the IPDF funding from the University of Sydney. Hong was partly supported by her ARC (Australian Research Council) Future Fellowship (FT3), Algorithmics for Visual Analytics of Massive Complex Networks. Liotta was partly supported by MIUR project AMANDA (Algorithmics for MAssive and Networked DAta).

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Authors and Affiliations

  1. University of Sydney, Sydney, NSW, Australia

    Seok-Hee Hong & Peter Eades

  2. Kyoto University, Kyoto, Japan

    Naoki Katoh

  3. University of Perugia, Perugia, Italy

    Giuseppe Liotta

  4. ETH, Zurich, Switzerland

    Pascal Schweitzer

  5. Niigata University, Niigata, Japan

    Yusuke Suzuki

Authors
  1. Seok-Hee Hong
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  2. Peter Eades
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  3. Naoki Katoh
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  4. Giuseppe Liotta
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  5. Pascal Schweitzer
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  6. Yusuke Suzuki
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Correspondence to Seok-Hee Hong.

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Hong, SH., Eades, P., Katoh, N. et al. A Linear-Time Algorithm for Testing Outer-1-Planarity. Algorithmica 72, 1033–1054 (2015). https://doi.org/10.1007/s00453-014-9890-8

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  • DOI: https://doi.org/10.1007/s00453-014-9890-8

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