Clique Planar Graphs

We generalize the idea of extended triangles of a graph G by considering a family of completes of G instead of the clique family of G. We characterize Helly and 3 - Helly Planar Graphs using extended triangles. We prove that if a planar graph is a clique graph then any one of its extended triangles is a clique graph. Finally, we show the extended triangles of a planar graph which are clique graphs. Any one of the obtained characterizations are tested in O(n2) time.