Turán numbers of Berge trees
نویسندگان
چکیده
A classical conjecture of Erdős and Sós asks to determine the Turán number a tree. We consider variants this problem in settings hypergraphs multi-hypergraphs. In particular, for all k r, with r≥k(k−2), we show that any r-uniform hypergraph H more than n(k−1)r+1 hyperedges contains Berge copy tree edges different from k-edge star. This bound is sharp when r+1 divides n such values extremal hypergraphs.
منابع مشابه
Turán numbers for Berge - hypergraphs and related 1 extremal problems
4 Let F be a graph. We say that a hypergraph H is a Berge-F if there is a bijection 5 f : E(F )→ E(H) such that e ⊆ f(e) for every e ∈ E(F ). Note that Berge-F actually 6 denotes a class of hypergraphs. The maximum number of edges in an n-vertex r-graph 7 with no subhypergraph isomorphic to any Berge-F is denoted exr(n,Berge-F ). In this 8 paper we establish new upper and lower bounds on exr(n,...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2023
ISSN: ['1872-681X', '0012-365X']
DOI: https://doi.org/10.1016/j.disc.2022.113286