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

TL;DR

This paper introduces a polynomial delay algorithm for generating all potential maximal cliques in triconnected planar graphs, enabling efficient treewidth computation for general planar graphs.

Contribution

It presents a novel characterization of potential maximal cliques in triconnected planar graphs and combines it with existing algorithms for improved treewidth computation.

Findings

Algorithm runs in polynomial delay

Enables linear-time treewidth algorithms for planar graphs

Advances understanding of potential maximal cliques in 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{\'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.