Asymptotically optimal -packings of dense graphs via fractional -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 / 9 k 10 ) + o ( n ) has a fractional K k -decomposition and has a K k -packing which covers all but o ( n 2 ) edges.