2 problems

Let $\mathcal{I}(n,k)$ denote the set of intersecting families $\mathcal{F}\subseteq\binom{[n]}{k}$, and let a family be trivial if all its members contain a common element. Then,…

Let $d_X$ and $d_Y$ be sufficiently large integers, let $\delta\geq 1$ and $\delta',\delta”>0$, and let $\Sigma=X\sqcup Y$ be a $\delta$-approximately $(d_X,d_Y)$-biregular graph s…