Common-neighbourhood sampling bound
= Common-neighbourhood sampling bound
If a bipartite graph with parts $A,B$ has density at least $p$, then averaging ordered distinct $t$-tuples gives a common neighbourhood of size at least
$$
|B|\left(p-\frac{t-1}{|A|}\right)^t.
$$
In particular this is at least $p^t|B|/2$ when $|A|$ is sufficiently large compared with $t^2/p$.