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

June 14, 2025 Β· Declared Dead Β· πŸ› International Symposium on Parameterized and Exact Computation

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Authors Alexander Grigoriev, Yasuaki Kobayashi, Hisao Tamaki, Tom C. van der Zanden arXiv ID 2506.12635 Category cs.DS: Data Structures & Algorithms Citations 0 Venue International Symposium on Parameterized and Exact Computation Last Checked 5 months ago
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{Γ©} 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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