Bollobás–Eldridge degree-product packing conjecture

Let $H_1$ and $H_2$ be graphs, let $K_n$ be the complete graph on $n$ vertices, and write $\Delta(H_i)$ for the maximum degree of $H_i$. A packing of $(H_1,H_2)$ in $K_n$ is a pair of injections into $K_n$ whose induced edge sets are disjoint. Bollobás–Eldridge degree-product conjecture. If

$$(\Delta(H_1)+1)(\Delta(H_2)+1)\leq n+1,$$

then $(H_1,H_2)$ pack into $K_n$. The paper presents this as an important conjecture concerning packing two graphs under a maximum-degree condition; no resolution status is supplied in the stated context.