Discrete Math Seminar

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 …