2 problems

Let $r\geqslant 3$ be constant, let $p\leqslant n^{-2/r+o(1)}$, and let $m=\big\lfloor\binom{n}{r}p^{\binom{r}{2}}\big\rfloor$. Write $F_r(G(n,p))$ for the number of $K_r$-factors…

Let $t$ and $n$ be positive integers, and let $\textbf{G}=\{G_1,G_2,\ldots,G_{\frac{n}{t}\binom{t}{2}}\}$ be an $n$-vertex graph system. Rainbow Hajnal--Szemerédi conjecture. If ……