Cliques in Steiner systems

Abstract A partial Steiner (k,l)-system is a k-uniform hypergraph with the property that every l-element subset of V is contained in at most one edge of . In this paper we show that for given k,l and t there exists a partial Steiner (k,l)-system such that whenever an l-element subset from every edge is chosen, the resulting l-uniform hypergraph contains a clique of size t. As the main result of this note, we establish asymptotic lower and upper …