Geodesic
3-uniform hypergraphs without a cycle of length five
The electronic journal of combinatorics, Tome 27 (2020) no. 2
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In this paper we show that the maximum number of hyperedges in a $3$-uniform hypergraph on $n$ vertices without a (Berge) cycle of length five is less than $(0.254 + o(1))n^{3/2}$, improving an estimate of Bollobás and Győri. We obtain this result by showing that not many $3$-paths can start from certain subgraphs of the shadow.
DOI : 10.37236/8806
Classification : 05C65, 05C38, 05C30, 05C35
Mots-clés : Berge cycle, maximum number of hyperedges 
@article{10_37236_8806,
     author = {Beka Ergemlidze and Ervin Gy\H{o}ri and Abhishek Methuku},
     title = {3-uniform hypergraphs without a cycle of length five},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {2},
     doi = {10.37236/8806},
     zbl = {1444.05100},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8806/}
}
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Beka Ergemlidze; Ervin Győri; Abhishek Methuku. 3-uniform hypergraphs without a cycle of length five. The electronic journal of combinatorics, Tome 27 (2020) no. 2. doi: 10.37236/8806

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