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Turán numbers of Berge trees

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Title
Turán numbers of Berge trees
Author(s)
Győri, Ervin; Nika Salia; Casey Tompkins; Zamora, Oscar
Publication Date
2023-04
Journal
Discrete Mathematics, v.346, no.4
Publisher
Elsevier BV
Abstract
© 2022 Elsevier B.V.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 [Formula presented] 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.
URI
https://pr.ibs.re.kr/handle/8788114/13219
DOI
10.1016/j.disc.2022.113286
ISSN
0012-365X
Appears in Collections:
Pioneer Research Center for Mathematical and Computational Sciences(수리 및 계산과학 연구단) > Discrete Mathematics Group(이산 수학 그룹) > 1. Journal Papers (저널논문)
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