3 problems

Győri–Katona–Lemons conjecture. The upper bound should have the same form as in the case $k>r+1$, namely

Let $\mathcal{P}=P_{\ell_1}\cup\dots\cup P_{\ell_k}$ be a linear forest with $k\geq 2$ and $\ell_k\geq\dots\geq\ell_1\geq 3$. Write … For an $r$-uniform hypergraph, let…

Let $\ell,r$ be integers and let $k\geq 2$. Write … For an $r$-uniform hypergraph, let $\mathrm{ex}_r(n,\text{Berge-} kP_\ell)$ denote the maximum number of hyperedges in an $n$-ve…