星形森林边缘膨胀的广义图兰结果

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics 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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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.

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