Hypergraph Turán Numbers of Vertex Disjoint Cycles

The Turán 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(?₁,…,?_r) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length ?₁,…?_r,respectively,and C_l~((k))denote a k-uniform linear ...     

Surfaces with simple geodesics through a point

We study compact connected surfaces inm-dimensional Euclidean spaceE ^m (3 m 5) with a point through which every geodesic is aW-curve regarded as a curve in E^m.