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

2014/12/27 by Füredi, Zoltán, Özkahya, Lale
#05C35 #05C65 #05D05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1412.8083

Abstract

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 C_2k+1-free hypergraphs is of the order O(k²n^1+1/k), improving the upper bound of Györi and Lemons by a factor of Θ(k²). Similar bounds are shown for linear hypergraphs.

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