2 problems

Let $k\geq 4$ and $0<\delta\leq 1$. A linear $3$-graph is a $3$-uniform hypergraph in which any two edges share at most one vertex; for a linear $3$-graph $\mathcal{H}$ with $n$ ve…

Nine-vertex 2-core conjecture. Every sufficiently large Steiner triple system contains a 2-core on nine vertices.