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Min-k-planar Drawings of Graphs

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Graph Drawing and Network Visualization (GD 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14465))

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Abstract

The study of nonplanar drawings of graphs with restricted crossing configurations is a well-established topic in graph drawing, often referred to as beyond-planar graph drawing. One of the most studied types of drawings in this area are the k-planar drawings \((k \ge 1)\), where each edge cannot cross more than k times. We generalize k-planar drawings, by introducing the new family of min-k-planar drawings. In a min-k-planar drawing edges can cross an arbitrary number of times, but for any two crossing edges, one of the two must have no more than k crossings. We prove a general upper bound on the number of edges of min-k-planar drawings, a finer upper bound for \(k=3\), and tight upper bounds for \(k=1,2\). Also, we study the inclusion relations between min-k-planar graphs (i.e., graphs admitting min-k-planar drawings) and k-planar graphs.

Research started at the Summer Workshop on Graph Drawing (SWGD) 2022, and partially supported by: (i) University of Perugia, Ricerca Base, Proj. AIDMIX (2021) and RICBA22CB; (ii) MUR PRIN Proj. 2022TS4Y3N - “EXPAND: scalable algorithms for EXPloratory Analyses of heterogeneous and dynamic Networked Data”; (iii) MUR PRIN Proj. 2022ME9Z78 - “NextGRAAL: Next-generation algorithms for constrained GRAph visuALization”.

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Authors and Affiliations

  1. Università degli Studi di Perugia, Perugia, Italy

    Carla Binucci, Walter Didimo, Giuseppe Liotta & Alessandra Tappini

  2. University of Tübingen, Tübingen, Germany

    Aaron Büngener & Michael Kaufmann

  3. Università Roma Tre, Rome, Italy

    Giuseppe Di Battista

  4. University of Ottawa, Ottawa, Canada

    Vida Dujmović

  5. University of Sydney, Sydney, Australia

    Seok-Hee Hong

  6. Carleton University, Ottawa, Canada

    Pat Morin

Authors
  1. Carla Binucci
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  2. Aaron Büngener
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  3. Giuseppe Di Battista
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  4. Walter Didimo
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  5. Vida Dujmović
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  10. Alessandra Tappini
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Correspondence to Carla Binucci .

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Editors and Affiliations

  1. University Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. University of Ioannina, Osnabrück, Germany

    Markus Chimani

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Binucci, C. et al. (2023). Min-k-planar Drawings of Graphs. In: Bekos, M.A., Chimani, M. (eds) Graph Drawing and Network Visualization. GD 2023. Lecture Notes in Computer Science, vol 14465. Springer, Cham. https://doi.org/10.1007/978-3-031-49272-3_3

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  • DOI: https://doi.org/10.1007/978-3-031-49272-3_3

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