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On the 2-Bend Slope Number of 1-Planar Graphs

Authors Michael A. Bekos , Eleni Katsanou , Philipp Kindermann , Aikaterini Maria Ntasiou , Maria Eleni Pavlidi , Soeren Terziadis

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Graph theory
Keywords
  • k-bend drawings
  • 1-planar graphs
  • beyond planarity
  • slope number

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Abstract

While drawing planar graphs with few slopes and few bends is a well-studied problem, corresponding extensions to beyond-planar graphs still remain mostly unexplored. Motivated by this observation, in this work, we provide bounds on the slope number of biconnected 1-planar graphs when two bends are allowed along each edge. Our contribution is an incremental drawing algorithm that produces 2-bend 1-planar drawings of biconnected 1-plane graphs with maximum degree Δ using any prescribed set of Δ pairwise distinct slopes.

Cite As Get BibTex

Michael A. Bekos, Eleni Katsanou, Philipp Kindermann, Aikaterini Maria Ntasiou, Maria Eleni Pavlidi, and Soeren Terziadis. On the 2-Bend Slope Number of 1-Planar Graphs. In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.32

Author Details

Michael A. Bekos
  • University of Ioannina, Greece
Eleni Katsanou
  • National Technical University of Athens, Greece
Philipp Kindermann
  • Trier University, Germany
Aikaterini Maria Ntasiou
  • University of Ioannina, Greece
Maria Eleni Pavlidi
  • University of Ioannina, Greece
Soeren Terziadis
  • TU Munich, Germany

Funding

The work was partially funded by the IKYDA 2025 funding program of the DAAD (project 57775422 "Algorithms and Combinatorics for Drawing Graphs with Few Slopes").

References

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