Abstract
Let p, q be two positive integers. The 3-graph F(p, q) is obtained from the complete 3-graph K 3p by adding q new vertices and \(p(_2^q)\) new edges of the form vxy for which v ∈ V(K 3p ) 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.
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The authors declare no conflict of interest.
This paper is supported by the National Natural Science Foundation of China (No. 12171089).
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Chang, A., Gao, Gr. On the Turán Density of Uniform Hypergraphs. Acta Math. Appl. Sin. Engl. Ser. 39, 638–646 (2023). https://doi.org/10.1007/s10255-023-1067-2
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DOI: https://doi.org/10.1007/s10255-023-1067-2