The Turán number of the triangular pyramid of 4-layers
Abstract
The Turán number $ex(n,H)$ 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 $TP_k$, 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 $ex(n, TP_4)=\frac{1}{4}n^2+Θ(n^{\frac{4}{3}})$. In this note, we confirm this conjecture.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 February 2026
- Language
- EN
- Document type
- Preprint