The bounded-degree spanning graph threshold conjecture

Fix a constant $\Delta$, and let $H=(H_n)$ be a sequence of graphs with maximum degree $\Delta(H)\le \Delta$ and at most $n$ vertices, $v(H)\le n$.

Bounded-degree spanning graph threshold conjecture. The random graph $G(n,p)$ almost surely contains $H$ whenever

$$p\cdot\frac{n^{2/(\Delta+1)}}{(\log n)^{1/\binom{\Delta+1}{2}}}\to\infty.$$

Equivalently, the conjectured threshold is the threshold for a $K_{\Delta+1}$-factor. The source says this optimum is widely believed and gives no resolution.