由一个环的爆破和一个星的爆破组成的族的Turán数

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2023-10-15 DOI:10.1007/s10114-023-1297-5

Zhi Wei Wu, Li Ying Kang

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引用次数: 0

摘要

设\（｛\cal F｝＝\｛H_1｝，\ldots，｛H_k｝\｝\，\，（k\ge1）\）是一个图族。族\（｛\cal F｝\）的Turán数是n-顶点｛H1，…，Hk｝-自由图中的最大边数，用ex（n，\（｛\cal F｛\））或ex（n、｛H1、H2、…，Hk｝）表示。图H的爆破是通过用相同大小的团替换H中的每条边而从H获得的图，其中团的新顶点都不同。在本文中，我们根据由一个周期、一颗恒星和具有k边的线性森林组成的族的Turán数，确定了由一个循环的爆破和一颗恒星的爆破组成的族中的Turān数。

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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Turán Number of the Family Consisting of a Blow-up of a Cycle and a Blow-up of a Star

Let \({\cal F} = \{ {H_1}, \ldots ,{H_k}\} \,\,(k \ge 1)\) be a family of graphs. The Turán number of the family \({\cal F}\) is the maximum number of edges in an n-vertex {H₁, …, H_k}-free graph, denoted by ex(n, \({\cal F}\)) or ex(n, {H₁,H₂, … H_k}). The blow-up of a graph H is the graph obtained from H by replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. In this paper we determine the Turán number of the family consisting of a blow-up of a cycle and a blow-up of a star in terms of the Turán number of the family consisting of a cycle, a star and linear forests with k edges.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.