2 problems

Erdős's conjecture. For any $g\in\mathbb{N}$, if $N$ is admissible and sufficiently large in terms of $g$, then there is a Steiner triple system which has no $(j,j-2)$-configuratio…

Let $D'(k,q)$ be the hypergraph defined in the paper, and let its girth be the length of its shortest cycle. Girth conjecture for $D'(k,q)$. The hypergraph $D'(k,q)$ has girth at l…