Document Open Access Logo

Circular Outside-Obstacle Representations of 2-Trees (Poster Abstract)

Authors Stefan Felsner , Carolina Haase , Philipp Kindermann , William J. Lenhart

PDF

File

Thumbnail PDF
PDF
LIPIcs.GD.2026.46.pdf
  • Filesize: 0.91 MB
  • 5 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Obstacle Representations
  • Outerplanar Graphs
  • 2-Trees

Metrics

Abstract

An outside-obstacle representation (OOR) of a graph G places its vertices in the plane together with a single obstacle in the outer face such that two vertices are adjacent if and only if the segment between them avoids the obstacle. An OOR is reducible if every edge is incident to the outer face, which implies that every subgraph also admits an OOR. Resolving a conjecture of Firman et al. [GD 2022], we show that every outerplanar graph admits a reducible circular OOR, that is, one with all vertices co-circular. In contrast, we present a family of 2-trees that admits no such representation.

Cite As Get BibTex

Stefan Felsner, Carolina Haase, Philipp Kindermann, and William J. Lenhart. Circular Outside-Obstacle Representations of 2-Trees (Poster Abstract). In 34th International Symposium on Graph Drawing and Network Visualization (GD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 396, pp. 46:1-46:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.GD.2026.46

Author Details

Stefan Felsner
  • TU Berlin, Germany
Carolina Haase
  • Trier University, Germany
Philipp Kindermann
  • Trier University, Germany
William J. Lenhart
  • Williams College, Williamstown, MA, USA

Acknowledgements

This work started at the Bertinoro Workshop on Graph Drawing (BWGD) 2026.

References

  1. Hannah Alpert, Christina Koch, and Joshua D. Laison. Obstacle numbers of graphs. Discr. Comput. Geom., 44(1):223-244, 2009. URL: https://doi.org/10.1007/s00454-009-9233-8.
  2. Martin Balko, Steven Chaplick, Robert Ganian, Siddharth Gupta, Michael Hoffmann, Pavel Valtr, and Alexander Wolff. Bounding and computing obstacle numbers of graphs. In Shiri Chechik, Gonzalo Navarro, Eva Rotenberg, and Grzegorz Herman, editors, Proc. 30th Ann. Europ. Symp. Algorithms (ESA'22), volume 244 of LIPIcs, pages 11:1-11:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPIcs.ESA.2022.11.
  3. Martin Balko, Steven Chaplick, Robert Ganian, Siddharth Gupta, Michael Hoffmann, Pavel Valtr, and Alexander Wolff. Bounding and computing obstacle numbers of graphs. SIAM J. Discret. Math., 38(2):1537-1565, 2024. URL: https://doi.org/10.1137/23M1585088.
  4. Oksana Firman, Philipp Kindermann, Jonathan Klawitter, Boris Klemz, Felix Klesen, and Alexander Wolff. Outside-obstacle representations with all vertices on the outer face. In Patrizio Angelini and Reinhard von Hanxleden, editors, Proc. 30th Int. Symp. Graph Drawing and Network Visualization (GD'22), volume 13764 of Lecture Notes in Computer Science, pages 432-440. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22203-0_31.
  5. Oksana Firman, Philipp Kindermann, Jonathan Klawitter, Boris Klemz, Felix Klesen, and Alexander Wolff. Outside-obstacle representations with all vertices on the outer face. Comput. Geom. Topol., 4(1):2:1-2:21, 2025. URL: https://doi.org/10.57717/CGT.V4I1.64.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact