Large forbidden trade volumes and edge packings of random graphs

Let G be a graph. A G-trade of volume m is a pair (T,T^'), where each of T and T^' consists of m graphs, pairwise edge-disjoint, isomorphic to G, such that [email protected]?T^'[email protected] and the union of the edge sets of the graphs in T is identical to the union of the edge sets of the graphs in T^'. Let X(G) be the set of non-negative integers m such that no G-trade of volume m exists. In this paper we prove that, for [email protected]?G(n,12),{1,2,...,@?cn/[email protected]?}@?X(G) holds asymptotically almost surely, where c=log(4/3)/88.