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 T ∩T ′ = ∅ 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 G ∈ G(n, 12 ), {1, 2, . . . , cn/ log n } ⊆ X(G) holds asymptotically almost surely, where c = log(4/3)/88.