2 problems

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 ……

Aharoni–Howard's conjecture. If each $H_i$ has $f(n,r,k)$ hyperedges, then there is a rainbow matching