The maximum number of copies of any hypergraph H in Berge-K_k-free r-graphs is achieved by the balanced complete (k-1)-partite r-graph for all sufficiently large k, with related bounds connecting hypergraph and graph cases.
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math.CO 2years
2026 2verdicts
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The connected Turán numbers for Berge paths and Berge cycles in r-uniform hypergraphs hold exactly for all k ≥ 2r+2 and fail for smaller k.
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Generalized Tur\'an problems for Berge hypergraphs
The maximum number of copies of any hypergraph H in Berge-K_k-free r-graphs is achieved by the balanced complete (k-1)-partite r-graph for all sufficiently large k, with related bounds connecting hypergraph and graph cases.
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On the connected Tur\'an number of Berge paths and Berge cycles
The connected Turán numbers for Berge paths and Berge cycles in r-uniform hypergraphs hold exactly for all k ≥ 2r+2 and fail for smaller k.