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2-Layer k-Planar Graphs

Density, Crossing Lemma, Relationships, and Pathwidth

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Graph Drawing and Network Visualization (GD 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12590))

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Abstract

The 2-layer drawing model is a well-established paradigm to visualize bipartite graphs. Several beyond-planar graph classes have been studied under this model. Surprisingly, however, the fundamental class of k-planar graphs has been considered only for \(k=1\) in this context. We provide several contributions that address this gap in the literature. First, we show tight density bounds for the classes of 2-layer k-planar graphs with \(k\in \{2,3,4,5\}\). Based on these results, we provide a Crossing Lemma for 2-layer k-planar graphs, which then implies a general density bound for 2-layer k-planar graphs. We prove this bound to be almost optimal with a corresponding lower bound construction. Finally, we study relationships between k-planarity and h-quasiplanarity in the 2-layer model and show that 2-layer k-planar graphs have pathwidth at most \(k+1\).

G. Da Lozzo—The work of Giordano Da Lozzo was partially supported by MIUR grants 20157EFM5C “MODE: MOrphing graph Drawings Efficiently” and 20174LF3T8 “AHeAD: efficient Algorithms for HArnessing networked Data”.

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Author information

Authors and Affiliations

  1. John Cabot University, Rome, Italy

    Patrizio Angelini

  2. Roma Tre University, Rome, Italy

    Giordano Da Lozzo

  3. University of Tübingen, Tübingen, Germany

    Henry Förster & Thomas Schneck

Authors
  1. Patrizio Angelini
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  2. Giordano Da Lozzo
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  3. Henry Förster
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  4. Thomas Schneck
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Corresponding author

Correspondence to Henry Förster .

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Editors and Affiliations

  1. LaBRI, University of Bordeaux, Talence, France

    David Auber

  2. Charles University, Prague, Czech Republic

    Pavel Valtr

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Angelini, P., Da Lozzo, G., Förster, H., Schneck, T. (2020). 2-Layer k-Planar Graphs. In: Auber, D., Valtr, P. (eds) Graph Drawing and Network Visualization. GD 2020. Lecture Notes in Computer Science(), vol 12590. Springer, Cham. https://doi.org/10.1007/978-3-030-68766-3_32

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  • DOI: https://doi.org/10.1007/978-3-030-68766-3_32

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