On the Turan 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-p(3) by adding q new vertices and p(q2) new edges of the form vxy for which v epsilon V (K-p(3)) and fx; yg are new vertices. It frequently appears in many literatures on the Turan number or Turan 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 Turan density under some situations. Moreover, we investigate the Turan density of the F (p; q) for small p; q and obtain some new bounds on their Turan densities.