Set Systems with No Singleton Intersection
Set Systems with No Singleton Intersection
Let $\mathcal{F}$ be a k‐uniform set system defined on a ground set of size n with no singleton intersection; i.e., no pair $A,B\in\mathcal{F}$ has $|A\cap B|=1$. Frankl showed that $|\mathcal{F}|\leq\binom{n-2}{k-2}$ for $k\geq4$ and n sufficiently large, confirming a conjecture of Erdo˝s and Sós. We determine the maximum size of $\mathcal{F}$ …