Problems and Results on Intersections of Set Systems of Structural Type

The study of intersection theorems for set systems was started in the papers of [BE 1] and [EKR 1] . In the last twenty years a fairly extended theory has developed, several survey papers [EK 1], [K] were written . There is also a forthcoming book [FFK 1] about extremal problems of set systems . Intersection theorems of structural type started in the papers of [SS 1] were followed by several others [SS 2] [SS 3] [SS 4] [R 1] [CFGS 1] [FSS 1] . The structures considered are mostly graphs or subsets of integers and the intersection properties are given in graph theoretical or arithmetical terms . The general problem is the following: Let S be an n-element set, and J be a family of subsets of S . J will be called the intersection family .