On a packing problem of Alon and Yuster

Two graphs G1G1 and G2G2, each on nn vertices, pack   if there exists a bijection ff from V(G1)V(G1) onto V(G2)V(G2) such that uv∈E(G1)uv∈E(G1) only if f(u)f(v)∉E(G2)f(u)f(v)∉E(G2). In 2014, Alon and Yuster proved that, for sufficiently large nn, if |E(G1)|