{"title":"Ramsey Numbers of a Wheel of Order Five Versus Fans","authors":"Yiyuan Hao, Chunlin You","doi":"10.1007/s41980-023-00833-0","DOIUrl":null,"url":null,"abstract":"<p>For graphs <i>G</i> and <i>H</i>, the Ramsey number <i>r</i>(<i>G</i>, <i>H</i>) is the smallest number <i>N</i>, such that any red/blue edge-coloring of <span>\\(K_N\\)</span> contains either a red copy of <i>G</i> or a blue copy of <i>H</i>. Let <span>\\(F_n=K_1+nK_2\\)</span> be a fan and <span>\\(W_4=K_1+C_4\\)</span> be a wheel of order five. In this paper, we show that the Ramsey number <span>\\(r(W_4,F_n)=4n+1\\)</span> for all sufficiently large <i>n</i>. Moreover, this implies that a large fan <span>\\(F_n\\)</span> is <span>\\(W_4\\)</span>-good.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-023-00833-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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