3 problems

Tight upper-bound conjecture. For all $k\geq2$,

The asymptotic upper-bound conjecture. The upper bound is the correct value:

Let $r$, $s$, $t$, $k$ be positive integers. A $t$-colouring assigns one of $t$ colours to every edge of a complete $r$-uniform hypergraph, and an $s$-coloured matching of size $k$…