On 3-Uniform Hypergraphs Without A Cycle Of A Given Length
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We study the maximum number of hyperedges in a 3-uniform hypergraph on n vertices that does not contain a Berge cycle of a given length l. In particular we prove that the upper bound for C2k+1-free hypergraphs is of the order O(k(2)n(1+1/k)), improving the upper bound of Gyori and Lemons (2012) by a factor of Theta (k(2)). Similar bounds are shown for linear hypergraphs. (C) 2016 Elsevier B.V. All rights reserved.