H-Factors in Dense Graphs

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