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The maximum size of intersecting k-graphs with covering number k
Abstract
Let m(k) be the maximum size of an intersecting k-graph with covering number k. In the present paper, it is proved that for all k>e32, m(k)≥ kkexp(−50√(klog k)). Together with Zakharov's upper bound \cite{Z}, this implies m(k)=kkexp(−k1/2+o(1)).
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BibTeX
@misc{frankl2026maximum,
title = {{The maximum size of intersecting $k$-graphs with covering number $k$}},
author = {Peter Frankl and Jian Wang and Yaoran Yang and Yutong Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37315},
eprint = {2610.37315},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37315},
}
RIS
TY - UNPB
TI - The maximum size of intersecting k-graphs with covering number k
AU - Peter Frankl
AU - Jian Wang
AU - Yaoran Yang
AU - Yutong Zhang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37315
UR - https://arxiv.org/abs/2610.37315
AB - Let m(k) be the maximum size of an intersecting k-graph with covering number k. In the present paper, it is proved that for all k>e^32, m(k)≥ k^kexp(−50√(klog k)). Together with Zakharov's upper bound \cite{Z}, this implies m(k)=k^kexp(−k^1/2+o(1)).
ER -