Danila Cherkashin, Alexey Gordeev, Georgii Strukov
{"title":"无 H 超图的 Erdős-Hajnal 问题","authors":"Danila Cherkashin, Alexey Gordeev, Georgii Strukov","doi":"10.1007/s00373-023-02737-6","DOIUrl":null,"url":null,"abstract":"<p>This paper deals with the minimum number <span>\\(m_H(r)\\)</span> of edges in an <i>H</i>-free hypergraph with the chromatic number more than <i>r</i>. We show how bounds on Ramsey and Turán numbers imply bounds on <span>\\(m_H(r)\\)</span>.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Erdős–Hajnal Problem for H-Free Hypergraphs\",\"authors\":\"Danila Cherkashin, Alexey Gordeev, Georgii Strukov\",\"doi\":\"10.1007/s00373-023-02737-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper deals with the minimum number <span>\\\\(m_H(r)\\\\)</span> of edges in an <i>H</i>-free hypergraph with the chromatic number more than <i>r</i>. We show how bounds on Ramsey and Turán numbers imply bounds on <span>\\\\(m_H(r)\\\\)</span>.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00373-023-02737-6\",\"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/10.1007/s00373-023-02737-6","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
本文讨论了色度数大于 r 的无 H 超图中边的最小数量 \(m_H(r)\)。我们展示了拉姆齐数和图兰数的约束是如何暗示 \(m_H(r)\)的约束的。
This paper deals with the minimum number \(m_H(r)\) of edges in an H-free hypergraph with the chromatic number more than r. We show how bounds on Ramsey and Turán numbers imply bounds on \(m_H(r)\).