{"title":"可忽略障碍与Turán指数","authors":"T. Jiang, Zilin Jiang, Jie Ma","doi":"10.4208/aam.OA-2022-0008","DOIUrl":null,"url":null,"abstract":"We show that for every rational number $r \\in (1,2)$ of the form $2 - a/b$, where $a, b \\in \\mathbb{N}^+$ satisfy $\\lfloor a/b \\rfloor^3 \\le a \\le b / (\\lfloor b/a \\rfloor +1) + 1$, there exists a graph $F_r$ such that the Turan number $\\operatorname{ex}(n, F_r) = \\Theta(n^r)$. Our result in particular generates infinitely many new Turan exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.","PeriodicalId":58853,"journal":{"name":"应用数学年刊:英文版","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Negligible Obstructions and Turán Exponents\",\"authors\":\"T. Jiang, Zilin Jiang, Jie Ma\",\"doi\":\"10.4208/aam.OA-2022-0008\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that for every rational number $r \\\\in (1,2)$ of the form $2 - a/b$, where $a, b \\\\in \\\\mathbb{N}^+$ satisfy $\\\\lfloor a/b \\\\rfloor^3 \\\\le a \\\\le b / (\\\\lfloor b/a \\\\rfloor +1) + 1$, there exists a graph $F_r$ such that the Turan number $\\\\operatorname{ex}(n, F_r) = \\\\Theta(n^r)$. Our result in particular generates infinitely many new Turan exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.\",\"PeriodicalId\":58853,\"journal\":{\"name\":\"应用数学年刊:英文版\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"应用数学年刊:英文版\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://doi.org/10.4208/aam.OA-2022-0008\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"应用数学年刊:英文版","FirstCategoryId":"1089","ListUrlMain":"https://doi.org/10.4208/aam.OA-2022-0008","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
摘要
我们证明，对于形式为$2 - a/b$的每个有理数$r \in (1,2)$，其中$a, b \in \mathbb{N}^+$满足$\lfloor a/b \rfloor^3 \le a \le b / (\lfloor b/a \rfloor +1) + 1$，存在一个图$F_r$，使得图兰数$\operatorname{ex}(n, F_r) = \Theta(n^r)$。我们的结果产生了无穷多个新的图兰指数。作为副产品，我们在最近的Bukh- Conlon猜想工作中形成了一个框架。
We show that for every rational number $r \in (1,2)$ of the form $2 - a/b$, where $a, b \in \mathbb{N}^+$ satisfy $\lfloor a/b \rfloor^3 \le a \le b / (\lfloor b/a \rfloor +1) + 1$, there exists a graph $F_r$ such that the Turan number $\operatorname{ex}(n, F_r) = \Theta(n^r)$. Our result in particular generates infinitely many new Turan exponents. As a byproduct, we formulate a framework that is taking shape in recent work on the Bukh--Conlon conjecture.
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