Bounded Fractional Intersecting Families are Linear in Size

• Published in: The Electronic journal of combinatorics Vol. 32; no. 3
• Main Authors: Balachandran, Niranjan, Das, Shagnik, Sankarnarayanan, Brahadeesh
• Format: Journal Article
• Language: English
• Published: 22.08.2025

Using the sunflower method, we show that if $\theta \in (0,1) \cap \mathbb{Q}$ and $\mathcal{F}$ is a $O(n^{1/3})$-bounded $\theta$-intersecting family over $[n]$, then $\lvert \mathcal{F} \rvert = O(n)$, and that if $\mathcal{F}$ is $o(n^{1/3})$-bounded, then $\lvert \mathcal{F} \rvert \leq (\frac{...