Intersecting of Hypergraph

Question

I am beginner for studying hypergraph, I learn hypergraph from this site but it still not enough for me to understand about hypergraph (especially for intersecting hypergraph).

The hypergraph $G$ is t-intersecting if every two edges of $G$ have at least $t$ vertices in common.

Anyone can give example of 2-intersecting and 3-intersecting ? As well as references to learn about hypergraph

Answer 1

For $r\gt\frac t2,$ the hypergraph $K_{2r-t}^r$ (all $r$-element subsets of a $(2r-t)$-element set) is $t$-intersecting.

You can learn more about hypergraphs from the text Hypergraphs: Combinatorics of Finite Sets by Claude Berge.