A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs
Data Structures and Algorithms
2025-10-14 v3
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.
Cite
@article{arxiv.2506.12635,
title = {A polynomial delay algorithm generating all potential maximal cliques in triconnected planar graphs},
author = {Alexander Grigoriev and Yasuaki Kobayashi and Hisao Tamaki and Tom C. van der Zanden},
journal= {arXiv preprint arXiv:2506.12635},
year = {2025}
}
Comments
20 pages, 5 figures. A version with some omitted proofs is to appear in IPEC 2025 post-conference proceedings