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2-Layer Fan-Planarity in Polynomial Time

Authors Yasuaki Kobayashi , Yuto Okada

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LIPIcs.GD.2026.17.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • 2-layer drawing
  • fan-planar drawing
  • bipartite graphs

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Abstract

In this paper, we give a polynomial-time algorithm for deciding whether a bipartite graph admits a 2-layer fan-planar drawing. This resolves an open problem posed in several papers since 2015.

Cite As Get BibTex

Yasuaki Kobayashi and Yuto Okada. 2-Layer Fan-Planarity in Polynomial Time. In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 17:1-17:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.17

Author Details

Yasuaki Kobayashi
  • Hokkaido University, Sapporo, Japan
Yuto Okada
  • Nagoya University, Japan

Funding

  • Kobayashi, Yasuaki: JSPS KAKENHI Grant Numbers JP23K28034, JP24H00686, JP24H00697, JP26K02980.
  • Okada, Yuto: JST SPRING Grant Number JPMJSP2125 and JSPS KAKENHI Grant Number JP26KJ1299.

References

  1. Patrizio Angelini, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, and Maurizio Patrignani. 2-level quasi-planarity or how caterpillars climb (spqr-)trees. In Dániel Marx, editor, Proceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms, SODA 2021, pages 2779-2798. SIAM, 2021. URL: https://doi.org/10.1137/1.9781611976465.165.
  2. Patrizio Angelini, Giordano Da Lozzo, Henry Förster, and Thomas Schneck. 2-layer k-planar graphs density, crossing lemma, relationships and pathwidth. The Computer Journal, 67(3):1005-1016, 2024. URL: https://doi.org/10.1093/COMJNL/BXAD038.
  3. Michael A. Bekos and Luca Grilli. Fan-planar graphs. In Seok-Hee Hong and Takeshi Tokuyama, editors, Beyond Planar Graphs, Communications of NII Shonan Meetings, pages 131-148. Springer, 2020. URL: https://doi.org/10.1007/978-981-15-6533-5_8.
  4. Therese Biedl, Steven Chaplick, Michael Kaufmann, Fabrizio Montecchiani, Martin Nöllenburg, and Chrysanthi N. Raftopoulou. Layered fan-planar graph drawings. In Javier Esparza and Daniel Král', editors, 45th International Symposium on Mathematical Foundations of Computer Science, MFCS 2020, volume 170 of LIPIcs, pages 14:1-14:13, 2020. URL: https://doi.org/10.4230/LIPIcs.MFCS.2020.14.
  5. Carla Binucci, Markus Chimani, Walter Didimo, Martin Gronemann, Karsten Klein, Jan Kratochvíl, Fabrizio Montecchiani, and Ioannis G. Tollis. Algorithms and characterizations for 2-layer fan-planarity: From caterpillar to stegosaurus. Journal of Graph Algorithms and Applications, 21(1):81-102, 2017. URL: https://doi.org/10.7155/JGAA.00398.
  6. Carla Binucci, Emilio Di Giacomo, Walter Didimo, Fabrizio Montecchiani, Maurizio Patrignani, Antonios Symvonis, and Ioannis G. Tollis. Fan-planarity: Properties and complexity. Theoretical Computer Science, 589:76-86, 2015. URL: https://doi.org/10.1016/J.TCS.2015.04.020.
  7. Walter Didimo, Giuseppe Liotta, and Fabrizio Montecchiani. A survey on graph drawing beyond planarity. ACM Computing Surveys, 52(1):4:1-4:37, 2019. URL: https://doi.org/10.1145/3301281.
  8. Fedor V. Fomin, Petr A. Golovach, Tanmay Inamdar, Saket Saurabh, and Meirav Zehavi. Tight parameterized (in)tractability of layered crossing minimization: Subexponential algorithms and kernelization. In Kasper Green Larsen and Barna Saha, editors, Proceedings of the 2026 Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2026, Vancouver, BC, Canada, January 11-14, 2026, pages 4628-4643. SIAM, 2026. URL: https://doi.org/10.1137/1.9781611978971.168.
  9. Michael Kaufmann and Torsten Ueckerdt. The density of fan-planar graphs. The Electronic Journal of Combinatorics, 29(1), 2022. URL: https://doi.org/10.37236/10521.
  10. Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff. Recognizing 2-layer and outer k-planar graphs. CoRR, abs/2412.04042, 2024. URL: https://doi.org/10.48550/arXiv.2412.04042.
  11. Yasuaki Kobayashi, Yuto Okada, and Alexander Wolff. Recognizing 2-layer and outer k-planar graphs. In Oswin Aichholzer and Haitao Wang, editors, 41st International Symposium on Computational Geometry, SoCG 2025, volume 332 of LIPIcs, pages 65:1-65:16, 2025. URL: https://doi.org/10.4230/LIPIcs.SOCG.2025.65.
  12. Yasuaki Kobayashi and Hisao Tamaki. A faster fixed parameter algorithm for two-layer crossing minimization. Information Processing Letters, 116(9):547-549, 2016. URL: https://doi.org/10.1016/J.IPL.2016.04.012.
  13. Yuto Okada. Pathwidth of 2-layer k-planar graphs. Computing in Geometry and Topology, 5:3:1-3:8, February 2026. URL: https://doi.org/10.57717/cgt.v5i1.101.
  14. Kozo Sugiyama, Shojiro Tagawa, and Mitsuhiko Toda. Methods for visual understanding of hierarchical system structures. IEEE Transactions on Systems, Man, and Cybernetics, 11(2):109-125, 1981. URL: https://doi.org/10.1109/TSMC.1981.4308636.
  15. David R. Wood. 2-layer graph drawings with bounded pathwidth. Journal of Graph Algorithms and Applications, 27(9):843-851, 2023. URL: https://doi.org/10.7155/JGAA.00647.
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