The Turán Number of Berge-$K_4$ in 3-Uniform Hypergraphs

The characteristic polynomials of uniform double hyperstars and uniform hypertriangles

“…Just like for ordinary graphs, the spectrum of a hypergraph has a close relationship with the structure of the hypergraph. Since then, it has attracted the attention of many researchers and the spectral theory of (uniform) hypergraphs has developed rapidly, see e.g., [3,[11][12][13][14]19,[22][23][24][25].…”

The Turán numbers of two kinds of Berge hypergraphs

“…Gerbner 等 [7] 对于任意 n 和 k > r + 2, 给 出了 ex r (n, Berge-K k ) 的精确值. 当 r = 3 和 k = 4 时, Gyárfás [14] 和 Zhu 等 [22] 完全确定了 ex 3 (n, Berge-K 4 ) 的精确值. Kang 等 [17] 确定了当 r k − 1 和 r 2k + 2 时 ex r (n, Berge-(k + 1)K 2 ) 的精 确值, 并给出了当 k r 2k + 1 时 ex r (n, Berge-(k + 1)K 2 ) 的上界.…”