2019/04/14 by Ervin Győri, Győri, Ervin, Nika Salia +5 · 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 · pdf · doi:10.48550/arxiv.1904.06728
openalex publication_date 2019/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical conjecture of Erdős and Sós asks to determine the Turán number of a tree. We consider variants of this problem in the settings of hypergraphs and multi-hypergraphs. In particular, for all k and r, with r ≥ k (k-2), we show that any r-uniform hypergraph H with more than (n(k-1))/(r+1) hyperedges contains a Berge copy of any tree with k edges different from the k-edge star. This bound is sharp when r+1 divides n and for such values of n we determine the extremal hypergraphs.