2024/09/05 by Lin-Peng Zhang, Zhang, Lin-Peng, Hajo Broersma +7
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2409.03323
openalex publication_date 2024/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Let F be a family of r-uniform hypergraphs. Denote by \exconnr(n,F) the maximum number of hyperedges in an n-vertex connected r-uniform hypergraph which contains no member of F as a subhypergraph. Denote by BCk the Berge cycle of length k, and by BPk the Berge path of length k. Füredi, Kostochka and Luo, and independently Győri, Salia and Zamora determined \exconnr(n,BPk) provided k is large enough compared to r and n is sufficiently large. For the case k≤ r, Kostochka and Luo obtained an upper bound for \exconnr(n,BPk). In this paper, we continue investigating the case k≤ r. We precisely determine \exconnr(n,BPk) when n is sufficiently large and n is not a multiple of~r. For the case k=r+1, we determine \exconnr(n,BPk) asymptotically.