BjarneSchuelke

Katona's intersection theorem states that every intersecting family $\mathcal{F}{\subseteq }^{(k)}$ satisfies $|\partial \mathcal{F}|\ge |\mathcal{F}|$, where $\partial \mathcal{F}=\{F\setminus x:x\in F\in \mathcal{F}\}$ is the shadow of $\mathcal{F}$. Frankl conjectured that for $n>2k$ and every intersecting family $\mathcal{F}{\subseteq }^{(k)}$, there is some $i\in$ such that $|\partial \mathcal{F}(i)|\ge |\mathcal{F}(i)|$, where $\mathcal F(i)=\{F\setminus i:i\in F\in\mathcal …