3 problems

Let $\mathcal{F}$ be a $k$-uniform hypergraph, let $\nu(\mathcal{F})$ be its matching number, and let $\tau(\mathcal{F})$ be its covering number, the minimum size of a vertex set m…

Let $H$ be an $r$-uniform hypergraph. For an integer $m$, let $u^{(m)}(H)$ be the maximum size of a family of edges in which every two edges intersect in fewer than $m$ vertices,…

Let $H$ be a hypergraph of $d$-intervals, let $\tau_w(H)$ be its weighted covering number, and let $\nu_w(H)$ be its weighted matching number. Weighted covering conjecture. One sho…