Hypergraph Turan Numbers of Vertex Disjoint Cycles

The Turan number of a k-uniform hypergraph H, denoted by ex(k)(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-l((k)) denote the family of all k-uniform minimal cycles of length l, S(l(1), ..., l(r))) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length l(1), ..., l(r), respectively, and C-l((k)) denote a k-uniform linear cycle of length l. We determine precisely ex(k) (n; S(l(1), ..., l(r))) and ex(k) (n; C-l1((k))), ..., C-lr((k)) for sufficiently large n. Our results extend recent results of Furedi and Jiang who determined the Turan numbers for single k-uniform minimal cycles and linear cycles.