The Turán number of the triangular pyramid of 4-layers

Hangdi Chen; Yaojun Chen; Xiutao Zhu

paper

The Turán number of the triangular pyramid of 4-layers

arXiv:2602.07484

Abstract

The Turán number $e x (n, H)$ of a graph $H$ is the maximum number of edges in any $H$ -free graph on $n$ vertices. The triangular pyramid of $k$ -layers, denoted by $T P_{k}$ , is a generalization of a triangle. The Turán problems of a triangular pyramid with small layers have been studied widely by Liu (E-JC, 2013), Xiao, Katona, Xiao and Zamora (DAM, 2022), Ghosh, Győri, Paulos, Xiao and Zamora (DAM, 2022). Moreover, Ghosh et al. conjectured that $e x (n, T P_{4}) = \frac{1}{4} n^{2} + Θ (n^{\frac{4}{3}})$ . In this note, we confirm this conjecture.