星形森林边缘膨胀的广义图兰结果

Pub Date : 2024-07-02 DOI:10.1016/j.disc.2024.114149

Yuanpei Wang , Zhenyu Ni , Yichong Liu , Liying Kang

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引用次数: 0

摘要

给定一个图 H 和一个整数 p≥2，H 的边炸开 Hp+1 是将 H 中的每条边替换为 p+1 阶的簇后得到的图，其中簇的新顶点都是不同的。广义图兰数 ex(n,Km,F) 表示无 n 个顶点的 F 图中 Km 的最大副本数。本文确定了星形森林边缘膨胀的广义图兰数的精确值，并描述了足够大 n 的唯一图的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Generalized Turán results for edge blow-up of star forests

Given a graph H and an integer $p \geq 2$ , the edge blow-up $H^{p + 1}$ of H is the graph obtained by replacing each edge in H with a clique of order $p + 1$ , where the new vertices of the cliques are all distinct. The generalized Turán number $e x (n, K_{m}, F)$ denote the maximum number of copies of $K_{m}$ in an n-vertex F-free graph. In this paper, we determine the exact value of generalized Turán number for edge blow-up of star forests and characterize the unique graph for sufficiently large n.

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