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Packing in a hypergraph: Difference between revisions

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→Packing under the stronger condition: +"This has subsequently improved to 𝑛/3−𝑂(log ⁡𝑛/loglog ⁡𝑛) and (𝑛−4)/3" + 2 ref
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Any Steiner Triple System on ''n'' vertices contains a packing covering all vertices but at most <math>O(n^{1/2}\ln^{3/2}n)</math>.
 
This has subsequently improved to <math>n/3-O(\frac{\log n}{\log \log n})</math><ref>{{Cite journal |lastlast1=Keevash |firstfirst1=Peter |last2=Pokrovskiy |first2=Alexey |last3=Sudakov |first3=Benny |last4=Yepremyan |first4=Liana |date=2022-04-15 |title=New bounds for Ryser’sRyser's conjecture and related problems |url=https://www.ams.org/btran/2022-09-08/S2330-0000-2022-00092-3/ |journal=Transactions of the American Mathematical Society, Series B |language=en |volume=9 |issue=8 |pages=288–321 |doi=10.1090/btran/92 |issn=2330-0000}}</ref> and <math>\frac{n-4}{3}</math><ref>{{Cite journal |last=Montgomery |first=Richard |date=2023 |title=A proof of the Ryser-Brualdi-Stein conjecture for large even $n$ |url=https://arxiv.org/abs/2310.19779 |journal=[[ArXiv]] |doiarxiv=10.48550/ARXIV.2310.19779}}</ref>
 
==See also==
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| journal = Publ. Math. Debrecen
| volume = 10
| year = 19632022
| issue = 1–4 | pages = 10–13
| doi = 10.5486/PMD.1963.10.1-4.02 | url = http://www.renyi.hu/~p_erdos/1963-07.pdf
}}.
* {{Citation
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