Uniform Hypergraphs under Certain Intersection Constraints between Hyperedges

hypergraph H is an ( n, m )- hypergraph if it contains n vertices and m hyperedges, where n ≥ 1 and m ≥ 0 are two integers. Let k be a positive integer and let L be a set of nonnegative integers. A hypergraph H is k-uniform if all its hyperedges have the same size k , and H is L-intersecting if the number of common vertices of every two hyperedges belongs to L . In this paper, we propose and investigate the problem of estimating the maximum k among all k -uniform L -intersecting ( n, m )-hypergraphs for fixed n, m and L . We will provide some tight upper and lower bounds on k in terms of n, m and L .