On 3-uniform hypergraphs without a cycle of a given length

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• 作者：Zolt&aacute ; n Fü ; redi^a ; ^{z-furedi@math.uiuc.edu} ; Lale Ö ; zkahya^b ; ^{ozkahya@hacettepe.edu.tr}
• 关键词：Tur&aacute ; n number ; Triangles ; Cycles ; Extremal graphs ; Triple systems
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：216
• 期：part_P3
• 页码：582-588
• 全文大小：423 K
• 卷排序：216

文摘

We study the maximum number of hyperedges in a 3-uniform hypergraph on nn vertices that does not contain a Berge cycle of a given length ℓℓ. In particular we prove that the upper bound for C2k+1C2k+1-free hypergraphs is of the order O(k2n1+1/k)O(k2n1+1/k), improving the upper bound of Győri and Lemons (2012) by a factor of Θ(k2)Θ(k2). Similar bounds are shown for linear hypergraphs.