Turán顶点不相交三角形和五边形的数字

IF 0.8 3区 数学 Q2 MATHEMATICS
Fangfang Wu, Hajo Broersma, Shenggui Zhang, Binlong Li
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引用次数: 0

摘要

Turán数字,用ex (n, H)表示,是不包含图H作为子图的n个顶点上的图的最大边数。用kC表示k个顶点不相交拷贝的并集。本文给出了顶点不相交环的Turán个数的新结果。我们的第一个结果处理Turán顶点不相交三角形的数量ex (n, kC3)。当k≤4时,我们确定\(n \geq {k^{2}+5k \over 2}\)的Turán数ex(n, kC3),当k≥4时,n≥k2 + 2。此外,当k≤4时,我们给出了\(3k \leq n \leq {k^{2}+5k \over 2}\)下ex (n, kC3)的下界和上界,当k≥4时,3k≤n≤k2 + 2。接下来,我们给出了Turán顶点不相交的五边形个数的下界ex (n, kC5)。最后,我们确定了n = 5k时的Turán数ex (n, kC5),并对n的其他值提出了ex (n, kC5)的两个猜想。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Turán Numbers for Vertex-disjoint Triangles and Pentagons

The Turán number, denoted by ex (n, H), is the maximum number of edges of a graph on n vertices containing no graph H as a subgraph. Denote by kC the union of k vertex-disjoint copies of C. In this paper, we present new results for the Turán numbers of vertex-disjoint cycles. Our first results deal with the Turán number of vertex-disjoint triangles ex (n, kC3). We determine the Turán number ex(n, kC3) for \(n \geq {k^{2}+5k \over 2}\) when k ≤ 4, and nk2 + 2 when k ≥ 4. Moreover, we give lower and upper bounds for ex (n, kC3) with \(3k \leq n \leq {k^{2}+5k \over 2}\) when k ≤ 4, and 3knk2 + 2 when k ≥ 4. Next, we give a lower bound for the Turán number of vertex-disjoint pentagons ex (n, kC5). Finally, we determine the Turán number ex (n, kC5) for n = 5k, and propose two conjectures for ex (n, kC5) for the other values of n.

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来源期刊
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.
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