Geodesic
The structure of hypergraphs without long Berge cycles
Ervin Győri1 ; Nathan Lemons2 ; Nika Salia1 ; Oscar Zamora3 ; Ervin Győri ; Nathan Lemons ; Nika Salia ; Oscar Zamora
1Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary
2Theoretical Division, Los Alamos National Laboratory, New Mexico, USA
3Universidad de Costa Rica, San José, Costa Rica
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 767-771 
Ervin Győri; Nathan Lemons; Nika Salia; Oscar Zamora; Ervin Győri; Nathan Lemons; Nika Salia; Oscar Zamora. The structure of hypergraphs without long Berge cycles. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 767-771. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a63/
@article{AMUC_2019_88_3_a63,
     author = {Ervin Gy\H{o}ri and Nathan Lemons and Nika Salia and Oscar Zamora and Ervin Gy\H{o}ri and Nathan Lemons and Nika Salia and Oscar Zamora},
     title = { The structure of hypergraphs without long {Berge} cycles},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {767--771},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a63/}
}
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Voir la notice de l'article provenant de la source Comenius University

We study the structure of $r$-uniform hypergraphs containing no Berge cycles of length at least $k$ for $k \leq r$, and determine that such hypergraphs have some special substructure. In particular we determine the extremal number of such hypergraphs, giving an affirmative answer to the conjectured value when $k=r$ and giving a a simple solution to a recent result of Kostochka-Luo when $k < r$.