Let n≥k≥r+3 and H be an n-vertex r-uniform hypergraph. We show that if |H|>[Formula presented](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 K k−1 (r) .
- Berge cycles
- Extremal hypergraph theory
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics