Asymptotically optimal K_k-packing of dense graphs via fractional K_k-decompositions

Let H be a fixed graph. A fractional H-decomposition of a graph G is an assignment of nonnegative real weights to the copies of H in G such that for each e ∈ E (G), the sum of the weights of copies of H containing e is precisely one. An H-packing of a graph G is a set of edge disjoint copies of H in G. The following results are proved. For every fixed k > 2, every graph with n vertices and minimum degree at least n (1 - 1/9k¹⁰) + o (n) has a fractional K_k -decomposition and has a K_k-packing which covers all but o (n²) edges.