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On the Recognition of Outerplanar Graphs with Queue Number 1 (Poster Abstract)

Authors Michael A. Bekos , Thomas Depian , Stefan Felsner , Michael Kaufmann , Philipp Kindermann , Fabrizio Montecchiani , Maria Eleni Pavlidi , Alexandra Weinberger , Alexander Wolff , Johannes Zink

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LIPIcs.GD.2026.43.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graph theory
Keywords
  • stack layouts
  • queue layouts
  • outerplanar
  • outerpaths

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Abstract

A linear layout of a graph is defined as a total order of the vertices and a partition of the edges to pages. In a stack (queue) layout, no two edges on the same page may cross (nest). The stack (queue) number of a graph is the minimum number of pages required in a stack (queue) layout. Our focus is on characterizing and recognizing graphs that have both stack number 1 and queue number 1.

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Michael A. Bekos, Thomas Depian, Stefan Felsner, Michael Kaufmann, Philipp Kindermann, Fabrizio Montecchiani, Maria Eleni Pavlidi, Alexandra Weinberger, Alexander Wolff, and Johannes Zink. On the Recognition of Outerplanar Graphs with Queue Number 1 (Poster Abstract). In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 43:1-43:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.43

Author Details

Michael A. Bekos
  • University of Ioannina, Greece
Thomas Depian
  • TU Wien, Austria
Stefan Felsner
  • Technische Universität Berlin, Germany
Michael Kaufmann
  • University of Tübingen, Germany
Philipp Kindermann
  • Universität Trier, Germany
Fabrizio Montecchiani
  • University of Perugia, Italy
Maria Eleni Pavlidi
  • University of Ioannina, Greece
Alexandra Weinberger
  • FernUniversität in Hagen, Germany
Alexander Wolff
  • Universität Würzburg, Germany
Johannes Zink
  • Technische Universität München, Germany

Funding

Michael A. Bekos and Maria Eleni Pavlidi were supported by HFRI Grant No: 26320.
  • Depian, Thomas: Thomas Depian was supported by the Vienna Science and Technology Fund (WWTF) under grant ICT22-029.

Acknowledgements

This research was initiated at the Bertinoro Workshop on Graph Drawing 2026.

References

  1. Michael J. Bannister, William E. Devanny, Vida Dujmović, David Eppstein, and David R. Wood. Track layouts, layered path decompositions, and leveled planarity. Algorithmica, 81(4):1561-1583, 2019. URL: https://doi.org/10.1007/S00453-018-0487-5.
  2. Michael A. Bekos, Thomas Depian, Stefan Felsner, Michael Kaufmann, Philipp Kindermann, Fabrizio Montecchiani, Maria Eleni Pavlidi, Alexandra Weinberger, Alexander Wolff, and Johannes Zink. On the recognition of outerplanar graphs with queue number 1. arXiv Report, 2026. URL: https://arxiv.org/abs/2607.24297.
  3. Vida Dujmović and David R. Wood. On linear layouts of graphs. Discrete Math. Theor. Comput. Sci., 6(2):339-358, 2004. URL: https://doi.org/10.46298/DMTCS.317.
  4. Michael R. Garey and David S. Johnson. Complexity results for multiprocessor scheduling under resource constraints. SIAM J. Comput., 4(4):397-411, 1975. URL: https://doi.org/10.1137/0204035.
  5. Lenwood S. Heath and Arnold L. Rosenberg. Laying out graphs using queues. SIAM J. Comput., 21(5):927-958, 1992. URL: https://doi.org/10.1137/0221055.
  6. Sergey Pupyrev. A collection of existing results on stack and queue numbers. https://spupyrev.github.io/linearlayouts.html, 2020. Accessed: 2/19/2026.
  7. Maciej M. Sysło. Characterizations of outerplanar graphs. Discrete Math., 26(1):47-53, 1979. URL: https://doi.org/10.1016/0012-365X(79)90060-8.
  8. Alexandra Weinberger and Ji Zeng. What induces plane structures in complete graph drawings? In Maarten Löffler and Silvia Miksch, editors, Proc. 34th Int. Symp. Graph Drawing & Network Vis. (GD), volume 396 of LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2026. https://arxiv.org/abs/2603.08340, URL: https://doi.org/10.4230/LIPIcs.GD.2026.21.
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