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′)(T,T′), where each of TT and T′T′ consists of m graphs, pairwise edge-disjoint, isomorphic to G  , such that T∩T′=∅T∩T′=∅ and the union of the edge sets of the graphs in TT is identical to the union of the edge sets of the graphs in T′T′. Let X(G)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∈GG∈G(n,12),{1,2,…,⌈cn/logn⌉}⊆X(G) holds asymptotically almost surely, where c=log(4/3)/88c=log(4/3)/88.