Abstract
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 T6, where T6 is the graph obtained from the complete graph K6 by deleting a path with four edges.
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