@article{6064e9070b1c4aac8e7e890b95a935f9,
title = "On 2-connected hypergraphs with no long cycles",
abstract = "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 ≥ k ≥ 4r ≥ 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 ≥ k ≥ r ≥ 3.",
author = "Zolt{\'a}n F{\"u}redi and Alexandr Kostochka and Ruth Luo",
note = "Funding Information: ∗Supported in part by the Hungarian National Research, Development and Innovation Office NKFIH grant KH-130371, and by the Simons Foundation Collaboration Grant 317487. †Supported in part by NSF grant DMS-1600592 and grants 18-01-00353A and 19-01-00682 of the Russian Foundation for Basic Research. ‡Supported in part by NSF grant DMS-1902808 and by Award RB17164 of the Research Board of the University of Illinois at Urbana-Champaign. Funding Information: Supported in part by the Hungarian National Research, Development and Innovation Office NKFIH grant KH-130371, and by the Simons Foundation Collaboration Grant 317487.?Supported in part by NSF grant DMS-1600592 and grants 18-01-00353A and 19-01-00682 of the Russian Foundation for Basic Research.?Supported in part by NSF grant DMS-1902808 and by Award RB17164 of the Research Board of the University of Illinois at Urbana-Champaign.. Acknowledgment. We thank a referee for helpful comments. Publisher Copyright: {\textcopyright} The authors. Released under the CC BY license (International 4.0).",
year = "2019",
doi = "10.37236/8488",
language = "English (US)",
volume = "26",
journal = "Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "4",
}