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

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{é} 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.

20 pages, 5 figures. A version with some omitted proofs is to appear in IPEC 2025 post-conference proceedings