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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For large n, the maximum signless Laplacian spectral radius among n-vertex r-dimensional pure simplicial complexes without r-dimensional wheels is attained by specific extremal complexes, generalizing graph results and providing a spectral analogue of the Sós-Erdős-Brown theorem for r=2.
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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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Signless Laplacian spectral radius of simplicial complexes without $r$-dimensional wheels
For large n, the maximum signless Laplacian spectral radius among n-vertex r-dimensional pure simplicial complexes without r-dimensional wheels is attained by specific extremal complexes, generalizing graph results and providing a spectral analogue of the Sós-Erdős-Brown theorem for r=2.