On the Turán Density of Uniform Hypergraphs

Let p, q be two positive integers. The 3-graph F(p, q) is obtained from the complete 3-graph K ³_p by adding q new vertices and \(p(_2^q)\) new edges of the form vxy for which v ∈ V(K ³_p ) and {x, y} are new vertices. It frequently appears in many literatures on the Turán number or Turán density of hypergraphs. In this paper, we first construct a new class of r-graphs which can be regarded as a generalization of the 3-graph F(p, q), and prove that these r-graphs have the same Turán density under some situations. Moreover, we investigate the Turán density of the F(p, q) for small p, q and obtain some new bounds on their Turán densities.