2023/12/06 by Shoham Letzter, Amedeo Sgueglia, Letzter, Shoham +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2312.03856
openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f(r)(n;s,k) be the maximum number of edges in an n-vertex r-uniform hypergraph not containing a subhypergraph with k edges on at most s vertices. Recently, Delcourt and Postle, building on work of Glock, Joos, Kim, Kühn, Lichev and Pikhurko, proved that the limit limn → ∞ n-2 f(3)(n;k+2,k) exists for all k ≥ 2, solving an old problem of Brown, Erdős and Sós (1973). Meanwhile, Shangguan and Tamo asked the more general question of determining if the limit limn → ∞ n-t f(r)(n;k(r-t)+t,k) exists for all r>t≥ 2 and k ≥ 2. Here we make progress on their question. For every even k, we determine the value of the limit when r is sufficiently large with respect to k and t. Moreover, we show that the limit exists for k ∈ \5,7\ and all r > t ≥ 2.