The Turán number of the triangular pyramid of 4-layers
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910015299780608 |
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| author | Chen, Hangdi Chen, Yaojun Zhu, Xiutao |
| author_facet | Chen, Hangdi Chen, Yaojun Zhu, Xiutao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Turán number of the triangular pyramid of 4-layers Chen, Hangdi Chen, Yaojun Zhu, Xiutao Combinatorics 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. |
| title | The Turán number of the triangular pyramid of 4-layers |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.07484 |