Hypergraph Turán numbers of vertex disjoint cycles

الأصل · EN

The Turán number of a k-uniform hypergraph H, denoted by exₖ(n;H), is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph. Let Cℓ(k) denote the family of all k-uniform minimal cycles of length ℓ, S(ℓ₁,,ℓᵣ) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length ℓ₁,,ℓᵣ, respectively, and Cℓ(k) denote a k-uniform linear cycle of length ℓ. We determine precisely exₖ(n;S(ℓ₁,,ℓᵣ)) and exₖ(n;Cℓ₁(k),, Cℓᵣ(k)) for sufficiently large n. The results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.