{"title":"定向星的可诱导性","authors":"Ping Hu , Jie Ma , Sergey Norin , Hehui Wu","doi":"10.1016/j.jctb.2024.04.001","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the problem of maximizing the number of induced copies of an oriented star <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub></math></span> in digraphs of given size, where the center of the star has out-degree <em>k</em> and in-degree <em>ℓ</em>. The case <span><math><mi>k</mi><mi>ℓ</mi><mo>=</mo><mn>0</mn></math></span> was solved by Huang in <span>[11]</span>. Here, we asymptotically solve it for all other oriented stars with at least seven vertices.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"168 ","pages":"Pages 11-46"},"PeriodicalIF":1.2000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The inducibility of oriented stars\",\"authors\":\"Ping Hu , Jie Ma , Sergey Norin , Hehui Wu\",\"doi\":\"10.1016/j.jctb.2024.04.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the problem of maximizing the number of induced copies of an oriented star <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>ℓ</mi></mrow></msub></math></span> in digraphs of given size, where the center of the star has out-degree <em>k</em> and in-degree <em>ℓ</em>. The case <span><math><mi>k</mi><mi>ℓ</mi><mo>=</mo><mn>0</mn></math></span> was solved by Huang in <span>[11]</span>. Here, we asymptotically solve it for all other oriented stars with at least seven vertices.</p></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":\"168 \",\"pages\":\"Pages 11-46\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-01\",\"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/S0095895624000285\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/5/6 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/S0095895624000285","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/5/6 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider the problem of maximizing the number of induced copies of an oriented star in digraphs of given size, where the center of the star has out-degree k and in-degree ℓ. The case was solved by Huang in [11]. Here, we asymptotically solve it for all other oriented stars with at least seven vertices.
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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