Minor and minimum cycle bases of a 3-connected planar graph

In this paper, we prove that if any set of |E(G)| . |V (G)| +1 facial cycles of a 3-connected planar graph G embedded in the plane doesn.t form a minimum cycle base of G, then any minimum cycle base of G contains a separating cycle, and G has a minor isomorphic to T 6, where T 6 is the graph obtained from the complete graph K 6 by deleting a path with four edges.