Tur´an Problems for Berge-(k, p)-Fan Hypergraph*


Zhenyu NI,Liying KANG,Erfang SHAN.Tur´an Problems for Berge-(k, p)-Fan Hypergraph*[J].Chinese Annals of Mathematics B,2021,42(4):487~494
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Zhenyu NI; Liying KANG;Erfang SHAN


National Natural Science Foundation of China (Nos. 11871329,11971298).
Abstract: Let F be a graph. A hypergraph H is Berge-F if there is a bijection f : E(F) → E(H) such that e ? f(e) for every e ∈ E(F). A hypergraph is Berge-F-free if it does not contain a subhypergraph isomorphic to a Berge-F hypergraph. The authors denote the maximum number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by exr(n, Berge-F).A (k, p)-fan, denoted by Fk,p, is a graph on k(p ? 1) + 1 vertices consisting of k cliques with p vertices that intersect in exactly one common vertex. In this paper they determine the bounds of exr(n, Berge-F) when F is a (k, p)-fan for k ≥ 2, p ≥ 3 and r ≥ 3.


Berge-hypergraph, Tur´an number


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