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Hypergraphs are generalizations of graphs, where edges can be made of more than two vertices.

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Turan numbers of r-partite hypergraphs

Let $H$ be a balanced $r$-partite $r$-uniform hypergraph with $nr$ vertices. (Each part of this hypergraph consists of $n$ vertices; every hyperedge has exactly one vertex in each part.) … Denote a complete balanced $r$-partite $r$-uniform hypergraph with $nr$ vertices as $K_{n}^r$. …