The Tur\'an Number of the Triangular Pyramid of $3$-Layers

Debarun Ghosh; Ervin Győri; Addisu Paulos; Chuanqi Xiao; Oscar Zamora

The Tur\'an Number of the Triangular Pyramid of $3$-Layers

Combinatorics 2021-07-22 v1

Authors: Debarun Ghosh , Ervin Győri , Addisu Paulos , Chuanqi Xiao , Oscar Zamora

Abstract

The Tur\'an number of a graph $H$ , denoted by $\text{ex}(n, H)$ , is the maximum number of edges in an $n$ -vertex graph that does not have $H$ as a subgraph. Let $TP_k$ be the triangular pyramid of $k$ -layers. In this paper, we determine that $\text{ex}(n,TP_3)= \frac{1}{4}n^2+n+o(n)$ and pose a conjecture for $\text{ex}(n,TP_4)$ .

Keywords

Turán number triangular pyramid extremal graph theory graph subgraph conjecture

Cite

@article{arxiv.2107.10229,
  title  = {The Tur\'an Number of the Triangular Pyramid of $3$-Layers},
  author = {Debarun Ghosh and Ervin Győri and Addisu Paulos and Chuanqi Xiao and Oscar Zamora},
  journal= {arXiv preprint arXiv:2107.10229},
  year   = {2021}
}

The Tur\'an Number of the Triangular Pyramid of $3$-Layers

Abstract

Keywords

Cite

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