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An edge of a -connected graph is said to be -contractible (or simply contractible) if the graph obtained from by contracting (i.e., deleting and identifying its ends, finally, replacing each of the resulting pairs of double edges by a single edge) is still -connected. In 2002, Kawarabayashi proved that for any odd integer , if is a -connected graph and contains no subgraph , then has a -contractible edge. In this paper, by generalizing this result, we prove that for any integer...
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