Geodesic
On hypergraphs of girth five
The electronic journal of combinatorics, Tome 10 (2003)
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In this paper, we study $r$-uniform hypergraphs ${\cal H}$ without cycles of length less than five, employing the definition of a hypergraph cycle due to Berge. In particular, for $r = 3$, we show that if ${\cal H}$ has $n$ vertices and a maximum number of edges, then $$|{\cal H}|={\textstyle 1\over6}n^{3/2} + o(n^{3/2}).$$ This also asymptotically determines the generalized Turán number $T_{3}(n,8,4)$. Some results are based on our bounds for the maximum size of Sidon-type sets in $\Bbb{Z}_{n}$.
DOI : 10.37236/1718
Classification : 05D05, 05D40, 05D99
Mots-clés : Turán number, Sidon-type sets 
@article{10_37236_1718,
     author = {Felix Lazebnik and Jacques Verstra\"ete},
     title = {On hypergraphs of girth five},
     journal = {The electronic journal of combinatorics},
     year = {2003},
     volume = {10},
     doi = {10.37236/1718},
     zbl = {1023.05131},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1718/}
}
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Felix Lazebnik; Jacques Verstraëte. On hypergraphs of girth five. The electronic journal of combinatorics, Tome 10 (2003). doi: 10.37236/1718

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