Abstract
Let n≥k≥r+3 and H be an n-vertex r-uniform hypergraph. We show that if|H|>n−1k−2(k−1r) then H contains a Berge cycle of length at least k. This bound is tight when k−2 divides n−1. We also show that the bound is attained only for connected r-uniform hypergraphs in which every block is the complete hypergraph Kk−1(r).
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