On the Ramsey number of the double star

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-08-30 DOI:10.1016/j.disc.2024.114227

Freddy Flores Dubó, Maya Stein

引用次数: 0

Abstract

The double star $S (m_{1}, m_{2})$ is obtained from joining the centres of a star with $m_{1}$ leaves and a star with $m_{2} \leq m_{1}$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S (m_{1}, m_{2})$ which holds for all $m_{1}, m_{2}$ with $\frac{\sqrt{5} + 1}{2} m_{2} < m_{1} < 3 m_{2}$ . Our result implies that for all positive m, the Ramsey number of the double star $S (2 m, m)$ is at most $⌈ 4.275 m ⌉ + 1$ .

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关于双星的拉姆齐数

双星 S(m1,m2) 是由一个有 m1 个叶子的星和一个有 m2≤m1 个叶子的星的中心连接而成。我们简短地证明了 S(m1,m2)的双色拉姆齐数的新上界，该上界在所有 m1,m2 为 5+12m2<m1<3m2 时都成立。我们的结果意味着，对于所有正 m，双星 S(2m,m) 的拉姆齐数最多为⌈4.275m↪Pe_2309+1。

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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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.