AlmostH-factors in dense graphs

The following asymptotic result is proved. For every?>0, and for every positive integerh, there exists ann0=n0(?, h) such that for every graphHwithhvertices and for everynn0, any graphGwithhnvertices and with minimum degreed?((?(H)?1)/?(H)+?)hncontainsnvertex disjoint copies ofH. This result is asymptotically tight and its proof supplies a polynomial time algorithm for the corresponding algorithmic problem.

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