3 problems

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…

Let $r$ and $k$ satisfy $k=r+1>2$, and let $\mathcal{H}$ be an $r$-uniform hypergraph, meaning that every hyperedge has size $r$. A Berge path of length $k$ consists of $k$ distinc…