Bollobás–Eldridge small-size graph packing conjecture

Let $H_1,H_2,\ldots,H_k$ be graphs and let $K_n$ be the complete graph on $n$ vertices. A packing of $(H_1,H_2,\ldots,H_k)$ in $K_n$ is a collection of injections of the graphs into $K_n$ whose induced edge sets are pairwise disjoint. Bollobás–Eldridge packing conjecture. If

$$|E(H_1)|,|E(H_2)|,\ldots,|E(H_k)|\leq n-k,$$

then $(H_1,H_2,\ldots,H_k)$ pack in $K_n$. The conjecture is known for $k=2$ and $k=3$, but remains open for $k\geq 4$ and is regarded as a major open problem in graph packing theory.