Hypergraph Turán Numbers of Vertex Disjoint Cycles

The Turán number of a k-uniform hypergraph H,denoted by ex;（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 C;denote the family of all k-uniform minimal cycles of length l;S（?;,…,?;） denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length ?;,…?;,respectively,and C;denote a k-uniform linear cycle of length l.We determine precisely ex;(n;S（?;,…,?;）) and exk(n;C;,…,C;for sufficiently large n.Our results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.