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Reeb Lobsters Are 1-Planar (Poster Abstract)

Authors Maarten Löffler , Miriam Münch , Ignaz Rutter

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graphs and surfaces
  • Mathematics of computing → Topology
Keywords
  • Reeb graphs
  • layered drawings
  • local crossing number

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Abstract

Very recently, Chambers, Fasy, Hosseini Sereshgi and Löffler [Erin W. Chambers et al., 2025] showed that every Reeb caterpillar admits a crossing-free drawing. It turns out that this does not hold for Reeb lobsters but we show that these graphs admit drawings with at most one crossing per edge.

Cite As Get BibTex

Maarten Löffler, Miriam Münch, and Ignaz Rutter. Reeb Lobsters Are 1-Planar (Poster Abstract). In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 50:1-50:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.50

Author Details

Maarten Löffler
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Miriam Münch
  • Faculty of Computer Science and Mathematics, University of Passau, Germany
Ignaz Rutter
  • Faculty of Computer Science and Mathematics, University of Passau, Germany

Funding

Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 541433306.

References

  1. Oliver Bastert and Christian Matuszewski. Layered Drawings of Digraphs, pages 87-120. Springer Berlin Heidelberg, Berlin, Heidelberg, 2001. URL: https://doi.org/10.1007/3-540-44969-8_5.
  2. Silvia Biasotti, Daniela Giorgi, Michela Spagnuolo, and Bianca Falcidieno. Reeb graphs for shape analysis and applications. Theoretical computer science, 392(1-3):5-22, 2008. URL: https://doi.org/10.1016/j.tcs.2007.10.018.
  3. Erin W. Chambers, Brittany Terese Fasy, Erfan Hosseini Sereshgi, and Maarten Löffler. Drawing reeb graphs. In Combinatorial Algorithms - 36th International Workshop, IWOCA 2025, volume 15885 of Lecture Notes in Computer Science, pages 58-71. Springer, 2025. URL: https://doi.org/10.1007/978-3-031-98740-3_5.
  4. William Harvey, Yusu Wang, and Rephael Wenger. A randomized O(m log m) time algorithm for computing Reeb graphs of arbitrary simplicial complexes. In Proceedings of the 2010 annual symposium on Computational geometry, SoCG '10, pages 267-276. ACM, 2010. URL: https://doi.org/10.1145/1810959.1811005.
  5. Salman Parsa. A deterministic O (m log m) time algorithm for the reeb graph. Discret. Comput. Geom., 49(4):864-878, 2013. URL: https://doi.org/10.1007/s00454-013-9511-3.
  6. Georges Reeb. Sur les points singuliers d'une forme de pfaff completement integrable ou d'une fonction numerique [on the singular points of a completely integrable pfaff form or of a numerical function]. Comptes Rendus Acad. Sciences Paris, 222:847-849, 1946. URL: https://cir.nii.ac.jp/crid/1571417125676878592.
  7. Kozo Sugiyama, Shôjirô Tagawa, and Mitsuhiko Toda. Methods for visual understanding of hierarchical system structures. IEEE Transactions on Systems, Man, and Cybernetics, SMC, 11(2):109-125, 1981. URL: https://doi.org/10.1109/TSMC.1981.4308636.
  8. Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz, and Bei Wang. Scalar field comparison with topological descriptors: Properties and applications for scientific visualization. In Computer Graphics Forum, volume 40, pages 599-633. Wiley Online Library, 2021. URL: https://doi.org/10.1111/cgf.14331.
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