{"title":"两个顶点不相连的小群副本的图兰数","authors":"Caiyun Hu","doi":"10.21136/cmj.2024.0461-23","DOIUrl":null,"url":null,"abstract":"<p>The Turán number of a given graph <i>H</i>, denoted by ex(<i>n, H</i>), is the maximum number of edges in an <i>H</i>-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(<i>n</i>, <i>K</i><sub><i>p</i></sub> ∪ <i>K</i><sub><i>q</i></sub>) of a vertex-disjoint union of cliques <i>K</i><sub><i>p</i></sub> and <i>K</i><sub><i>q</i></sub> for all values of <i>n</i>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Turán number of two vertex-disjoint copies of cliques\",\"authors\":\"Caiyun Hu\",\"doi\":\"10.21136/cmj.2024.0461-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The Turán number of a given graph <i>H</i>, denoted by ex(<i>n, H</i>), is the maximum number of edges in an <i>H</i>-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(<i>n</i>, <i>K</i><sub><i>p</i></sub> ∪ <i>K</i><sub><i>q</i></sub>) of a vertex-disjoint union of cliques <i>K</i><sub><i>p</i></sub> and <i>K</i><sub><i>q</i></sub> for all values of <i>n</i>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.21136/cmj.2024.0461-23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.21136/cmj.2024.0461-23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
给定图 H 的图兰数用 ex(n, H) 表示，是 n 个顶点上无 H 图中的最大边数。应用 Hajnal 和 Szemerédi 的一个著名结果，我们可以确定 Kp 和 Kq 的顶点二连联盟的图兰数 ex(n,Kp∪Kq)，且适用于所有 n 值。
Turán number of two vertex-disjoint copies of cliques
The Turán number of a given graph H, denoted by ex(n, H), is the maximum number of edges in an H-free graph on n vertices. Applying a well-known result of Hajnal and Szemerédi, we determine the Turán number ex(n, Kp ∪ Kq) of a vertex-disjoint union of cliques Kp and Kq for all values of n.
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