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A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs

Authors Alexander Grigoriev , Yasuaki Kobayashi , Hisao Tamaki , Tom C. van der Zanden

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LIPIcs.IPEC.2025.21.pdf
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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • potential maximal cliques
  • treewidth
  • planar graphs
  • triconnected planar graphs
  • polynomial delay generation

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Abstract

We develop a new characterization of potential maximal cliques of a triconnected planar graph and, using this characterization, give a polynomial delay algorithm generating all potential maximal cliques of a given triconnected planar graph. Combined with the dynamic programming algorithm due to Bouchitté and Todinca, this algorithm leads to a treewidth algorithm for general planar graphs that runs in time linear in the number of potential maximal cliques and polynomial in the number of vertices.

Cite As Get BibTex

Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, and Tom C. van der Zanden. A Polynomial Delay Algorithm Generating All Potential Maximal Cliques in Triconnected Planar Graphs. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.21

Author Details

Alexander Grigoriev
  • Department of Data Analytics and Digitalisation, Maastricht University, The Netherlands
Yasuaki Kobayashi
  • Hokkaido University, Sapporo, Japan
Hisao Tamaki
  • Meiji University, Kawasaki, Japan
Tom C. van der Zanden
  • Department of Data Analytics and Digitalisation, Maastricht University, The Netherlands

Funding

  • Kobayashi, Yasuaki: JSPS KAKENHI Grant Numbers JP23K28034, JP24H00686 and JP24H00697
  • Tamaki, Hisao: JSPS KAKENHI Grant Number JP24H00697

References

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