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arXiv · 2610.22021

The asymptotic Erd{ő}s--Frankl--Füredi cover-free conjecture

Xinqi Huang·Hong Liu
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Abstract

In 1985, Erd{ő}s, Frankl and F{ü}redi conjectured that the threshold $T(r)$ for the existence of an $r$-cover-free family with more members than points satisfies $T(r)=(1+o(1))r^2$. We confirm this conjecture by proving $T(r)\ge r^2+r+2$ for every $r\ge1$.

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Xinqi Huang, Hong Liu. 2026-10-15. The asymptotic Erd{ő}s--Frankl--Füredi cover-free conjecture. https://arxiv.org/abs/2610.22021

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