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이산수학 그룹
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General lemmas for Berge–Turán hypergraph problems

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Title
General lemmas for Berge–Turán hypergraph problems
Author(s)
Gerbner D.; Abhishek Methuku; Palmer C.
Publication Date
2020-05
Journal
European Journal of Combinatorics, v.86
Publisher
Elsevier
Abstract
For a graph F, a hypergraph H is a Berge copy of F (or a Berge-F in short), if there is a bijection f:E(F)→E(H) such that for each e∈E(F) we have e⊂f(e). A hypergraph is Berge-F-free if it does not contain a Berge copy of F. We denote the maximum number of hyperedges in an n-vertex r-uniform Berge-F-free hypergraph by exr(n,Berge-F). In this paper we prove two general lemmas concerning the maximum size of a Berge-F-free hypergraph and use them to establish new results and improve several old results. In particular, we give bounds on exr(n,Berge-F) when F is a path (reproving a result of Győri, Katona and Lemons), a cycle (extending a result of Füredi and Özkahya), a theta graph (improving a result of He and Tait), or a K2,t (extending a result of Gerbner, Methuku and Vizer). We establish new bounds when F is a clique (which implies extensions of results by Maherani and Shahsiah and by Gyárfás) and when F is a general tree
URI
https://pr.ibs.re.kr/handle/8788114/9074
DOI
10.1016/j.ejc.2020.103082
ISSN
0195-6698
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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