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The asymptotic Erd{ő}s--Frankl--Füredi cover-free conjecture
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))r2. We confirm this conjecture by proving T(r)≥ r2+r+2 for every r≥1.
Related
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BibTeX
@misc{huang2026asymptotic,
title = {{The asymptotic Erdős--Frankl--Füredi cover-free conjecture}},
author = {Xinqi Huang and Hong Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22021},
eprint = {2610.22021},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22021},
}
RIS
TY - UNPB
TI - The asymptotic Erd{ő}s--Frankl--Füredi cover-free conjecture
AU - Xinqi Huang
AU - Hong Liu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22021
UR - https://arxiv.org/abs/2610.22021
AB - 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)≥ r^2+r+2 for every r≥1.
ER -