We give an upper bound for the maximum number of edges in an $n$-vertex 2-connected $r$-uniform hypergraph with no Berge cycle of length $k$ or greater, where $n\ge k \ge 4r\ge 12$. For $n$ large with respect to $r$ and $k$, this bound is sharp and is significantly stronger than the bound without restrictions on connectivity. It turned out that it is simpler to prove the bound for the broader class of Sperner families where the size of each set is at most $r$. For such families, our bound is sharp for all $n\ge k\geq r\ge 3$.
@article{10_37236_8488,
author = {Zolt\'an F\"uredi and Alexandr Kostochka and Ruth Luo},
title = {On 2-connected hypergraphs with no long cycles},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {4},
doi = {10.37236/8488},
zbl = {1427.05150},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8488/}
}
TY - JOUR
AU - Zoltán Füredi
AU - Alexandr Kostochka
AU - Ruth Luo
TI - On 2-connected hypergraphs with no long cycles
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/8488/
DO - 10.37236/8488
ID - 10_37236_8488
ER -
%0 Journal Article
%A Zoltán Füredi
%A Alexandr Kostochka
%A Ruth Luo
%T On 2-connected hypergraphs with no long cycles
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/8488/
%R 10.37236/8488
%F 10_37236_8488
Zoltán Füredi; Alexandr Kostochka; Ruth Luo. On 2-connected hypergraphs with no long cycles. The electronic journal of combinatorics, Tome 26 (2019) no. 4. doi: 10.37236/8488
