Generalized Turan number for the edge blow-up graph

Zequn Lv; Ervin Győri; Zhen He; Nika Salia; Casey Tompkins; Kitti Varga; Xiutao Zhu

Generalized Turan number for the edge blow-up graph

Combinatorics 2022-10-24 v1

Authors: Zequn Lv , Ervin Győri , Zhen He , Nika Salia , Casey Tompkins , Kitti Varga , Xiutao Zhu

Abstract

Let $H$ be a graph and $p$ be an integer. The edge blow-up $H^p$ of $H$ is the graph obtained from replacing each edge in $H$ by a copy of $K_p$ where the new vertices of the cliques are all distinct. Let $C_k$ and $P_k$ denote the cycle and path of length $k$ , respectively. In this paper, we find sharp upper bounds for $ex(n,K_3,C_3^3)$ and the exact value for $ex(n,K_3,P_3^3)$ and determine the graphs attaining these bounds.

Keywords

generalized turan number edge blow-up graph extremal graph theory cycle path clique

Cite

@article{arxiv.2210.11914,
  title  = {Generalized Turan number for the edge blow-up graph},
  author = {Zequn Lv and Ervin Győri and Zhen He and Nika Salia and Casey Tompkins and Kitti Varga and Xiutao Zhu},
  journal= {arXiv preprint arXiv:2210.11914},
  year   = {2022}
}

Generalized Turan number for the edge blow-up graph

Abstract

Keywords

Cite

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