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arXiv · 2506.12635

A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs

Alexander Grigoriev·Yasuaki Kobayashi·Hisao Tamaki·Tom C. van der Zanden
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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 algorithms due to Bouchitt{\'e} 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.

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Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, Tom C. van der Zanden. 2025-06-14. A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs. https://arxiv.org/abs/2506.12635

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