Packing of graphs with small product of sizes

We show that for every ϵ > 0 , there exists n 0 = n 0 ( ϵ ) such that for every n > n 0 , two n-vertex graphs G 1 and G 2 with e ( G 1 ) e ( G 2 ) ⩽ ( 1 − ϵ ) n 2 pack, unless they belong to a well-defined family of exceptions. This extends a well-known result by Sauer and Spencer.