Peter Allen , Tomasz Łuczak , Joanna Polcyn , Yanbo Zhang
{"title":"长偶周期与恒星的拉姆齐数","authors":"Peter Allen , Tomasz Łuczak , Joanna Polcyn , Yanbo Zhang","doi":"10.1016/j.jctb.2023.05.001","DOIUrl":null,"url":null,"abstract":"<div><p>We find the exact value of the Ramsey number <span><math><mi>R</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span>, when <em>ℓ</em> and <span><math><mi>n</mi><mo>=</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>10</mn><mo>/</mo><mn>9</mn></mrow></msup><mo>)</mo></math></span> are large. Our result is closely related to the behaviour of Turán number <span><math><mrow><mi>ex</mi></mrow><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub><mo>)</mo></math></span> for an even cycle whose length grows quickly with <em>N</em>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"162 ","pages":"Pages 144-153"},"PeriodicalIF":1.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Ramsey number of a long even cycle versus a star\",\"authors\":\"Peter Allen , Tomasz Łuczak , Joanna Polcyn , Yanbo Zhang\",\"doi\":\"10.1016/j.jctb.2023.05.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We find the exact value of the Ramsey number <span><math><mi>R</mi><mo>(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>n</mi></mrow></msub><mo>)</mo></math></span>, when <em>ℓ</em> and <span><math><mi>n</mi><mo>=</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>10</mn><mo>/</mo><mn>9</mn></mrow></msup><mo>)</mo></math></span> are large. Our result is closely related to the behaviour of Turán number <span><math><mrow><mi>ex</mi></mrow><mo>(</mo><mi>N</mi><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>ℓ</mi></mrow></msub><mo>)</mo></math></span> for an even cycle whose length grows quickly with <em>N</em>.</p></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":\"162 \",\"pages\":\"Pages 144-153\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series B\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0095895623000412\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/5/29 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895623000412","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/5/29 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Ramsey number of a long even cycle versus a star
We find the exact value of the Ramsey number , when ℓ and are large. Our result is closely related to the behaviour of Turán number for an even cycle whose length grows quickly with N.
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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