Ramsey Numbers of Order Five vs Fans

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2023-11-18 DOI:10.1007/s41980-023-00833-0

Yiyuan Hao, Chunlin You

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引用次数: 0

摘要

对于图G和图H，拉姆齐数r(G, H)是最小的数N，使得\(K_N\)的任何红/蓝边着色都包含G的红色副本或H的蓝色副本。设\(F_n=K_1+nK_2\)为扇形，\(W_4=K_1+C_4\)为五阶轮盘。在本文中，我们证明了拉姆齐数\(r(W_4,F_n)=4n+1\)对于所有足够大的n。此外，这意味着一个大风扇\(F_n\)是\(W_4\) -好。

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Ramsey Numbers of a Wheel of Order Five Versus Fans

For graphs G and H, the Ramsey number r(G, H) is the smallest number N, such that any red/blue edge-coloring of \(K_N\) contains either a red copy of G or a blue copy of H. Let \(F_n=K_1+nK_2\) be a fan and \(W_4=K_1+C_4\) be a wheel of order five. In this paper, we show that the Ramsey number \(r(W_4,F_n)=4n+1\) for all sufficiently large n. Moreover, this implies that a large fan \(F_n\) is \(W_4\)-good.

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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.