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a b s t r a c tIn this paper, we proved the following result: Let G be a (korder at most t. This theorem generalizes some earlier results by Robertson, Seymour and Thomas [N. Robertson, P.D. Seymour, R. Thomas, Hadwiger conjecture for K 6 -free graphs, Combinatorica 13 (1993) 279-361.], Kawarabayashi and Toft [K. Kawarabayashi, B. Toft, Any 7-chromatic graph has K 7 or K 4,4 as a minor, Combinatorica 25 (2005) 327-353] On structure of k-connected graphs without K k -minor, Europ. J. Combinatorics 26 (2005) 293-308].