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

Xinqi Huang, Hong Liu

Source record

Source: arXiv

Published: Oct 15, 2026

arXiv: 2610.22021

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Source 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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The asymptotic Erd{ő}s--Frankl--Füredi cover-free conjecture — Mathematical Frontier Network