Asymptotically optimal Kk-packings of dense graphs via fractional Kk-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− 1/9k) + o(n) has a fractional Kk-decomposition and has a Kk-packing which covers all but o(n) edges.