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Linear-Time Vertex-Connectivity for Graphs of Bounded Genus

Authors Sergio Cabello , Alexander Dobler , Gašper Fijavž , Thekla Hamm , Mirko H. Wagner

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Fixed parameter tractability
Keywords
  • vertex-connectivity
  • graphs on surfaces
  • genus of a graph

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Abstract

We provide a new linear-time algorithm for determining the vertex-connectivity of graphs with bounded genus. This generalizes and streamlines a linear-time algorithm for graphs with bounded crossing number which was recently obtained by Biedl, Bose and Murali [ESA 2024]. Compared to applying the even more recent fixed parameter linear-time algorithm for deciding bounded vertex-connectivity announced by Korhonen [STOC 2025] to graphs of bounded genus,our algorithm is far simpler, its correctness easier to establish, and it makes use of geometric ideas, as is natural for surface-embedded graphs.

Cite As Get BibTex

Sergio Cabello, Alexander Dobler, Gašper Fijavž, Thekla Hamm, and Mirko H. Wagner. Linear-Time Vertex-Connectivity for Graphs of Bounded Genus. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 56:1-56:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.56

Author Details

Sergio Cabello
  • Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
  • Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
Alexander Dobler
  • TU Wien, Austria
Gašper Fijavž
  • Faculty of Computer and Information Science, University of Ljubljana, Slovenia
Thekla Hamm
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Mirko H. Wagner
  • Theoretical Computer Science, Osnabrück University, Germany

Funding

  • Cabello, Sergio: Funded in part by the Slovenian Research and Innovation Agency (P1-0297, N1-0218, N1-0285, J1-70045). Funded in part by the European Union (ERC, KARST, project number 101071836). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
  • Dobler, Alexander: Vienna Science and Technology Fund (WWTF) grant [10.47379/ICT19035].

Acknowledgements

This work was started during the Crossing Number Workshop 2024 that took place in Montserrat, Spain. We thank the organizers and participants for providing a fruitful research environment.

References

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