2019/01/31 by Zoltán Füredi, Furedi, Zoltan, Alexandr Kostochka +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · doi:10.48550/arxiv.1901.11159
openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.