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The Rique-Number of Graphs

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Graph Drawing and Network Visualization (GD 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13764))

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Abstract

We continue the study of linear layouts of graphs in relation to known data structures. At a high level, given a data structure, the goal is to find a linear order of the vertices of the graph and a partition of its edges into pages, such that the edges in each page follow the restriction of the given data structure in the underlying order. In this regard, the most notable representatives are the stack and queue layouts, while there exists some work also for deques.

In this paper, we study linear layouts of graphs that follow the restriction of a restricted-input queue (rique), in which insertions occur only at the head, and removals occur both at the head and the tail. We characterize the graphs admitting rique layouts with a single page and we use the characterization to derive a corresponding testing algorithm when the input graph is maximal planar. We finally give bounds on the number of needed pages (so-called rique-number) of complete graphs.

This work was initiated at the Bertinoro Workshop on Graph Drawing 2022.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Stefan Felsner

  3. Fachbereich IV - Informatikwissenschaften, Universität Trier, Trier, Germany

    Philipp Kindermann

  4. Department of Computer Science, University of Arizona, Tucson, AZ, USA

    Stephen Kobourov

  5. Department of Applied Mathematics, Charles University, Prague, Czech Republic

    Jan Kratochvíl

  6. Fakultät für Informatik und Mathematik, Universität Passau, Passau, Germany

    Ignaz Rutter

Authors
  1. Michael A. Bekos
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  2. Stefan Felsner
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  3. Philipp Kindermann
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  4. Stephen Kobourov
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  5. Jan Kratochvíl
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  6. Ignaz Rutter
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Corresponding author

Correspondence to Philipp Kindermann .

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Editors and Affiliations

  1. John Cabot University, Rome, Italy

    Patrizio Angelini

  2. Kiel University, Kiel, Germany

    Reinhard von Hanxleden

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Bekos, M.A., Felsner, S., Kindermann, P., Kobourov, S., Kratochvíl, J., Rutter, I. (2023). The Rique-Number of Graphs. In: Angelini, P., von Hanxleden, R. (eds) Graph Drawing and Network Visualization. GD 2022. Lecture Notes in Computer Science, vol 13764. Springer, Cham. https://doi.org/10.1007/978-3-031-22203-0_27

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  • DOI: https://doi.org/10.1007/978-3-031-22203-0_27

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