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 cont...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.展开更多
文摘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.