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.

翻译：本文提出了三连通平面图潜在极大团的新刻画方法，并基于该刻画给出了能够生成给定三连通平面图所有潜在极大团的延迟多项式算法。结合Bouchitté和Todinca提出的动态规划算法，该算法可推导出适用于一般平面图的树宽算法，其时间复杂度与潜在极大团数量呈线性关系，与顶点数量呈多项式关系。