{"title":"密集图中的跨细分","authors":"Hyunwoo Lee","doi":"10.1016/j.ejc.2024.104059","DOIUrl":null,"url":null,"abstract":"<div><p>We prove that an <span><math><mi>n</mi></math></span>-vertex digraph <span><math><mi>D</mi></math></span> with minimum semi-degree at least <span><math><mrow><mfenced><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>ɛ</mi></mrow></mfenced><mi>n</mi></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≥</mo><mi>C</mi><mi>m</mi></mrow></math></span> contains a subdivision of all <span><math><mi>m</mi></math></span>-arc digraphs without isolated vertices. Here, <span><math><mi>C</mi></math></span> is a constant only depending on <span><math><mrow><mi>ɛ</mi><mo>.</mo></mrow></math></span> This is the best possible and settles a conjecture raised by Pavez-Signé (2023) in a stronger form.</p></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0195669824001446/pdfft?md5=53af666a1aa86ffe42f097ee615130a5&pid=1-s2.0-S0195669824001446-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Spanning subdivisions in dense digraphs\",\"authors\":\"Hyunwoo Lee\",\"doi\":\"10.1016/j.ejc.2024.104059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove that an <span><math><mi>n</mi></math></span>-vertex digraph <span><math><mi>D</mi></math></span> with minimum semi-degree at least <span><math><mrow><mfenced><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>+</mo><mi>ɛ</mi></mrow></mfenced><mi>n</mi></mrow></math></span> and <span><math><mrow><mi>n</mi><mo>≥</mo><mi>C</mi><mi>m</mi></mrow></math></span> contains a subdivision of all <span><math><mi>m</mi></math></span>-arc digraphs without isolated vertices. Here, <span><math><mi>C</mi></math></span> is a constant only depending on <span><math><mrow><mi>ɛ</mi><mo>.</mo></mrow></math></span> This is the best possible and settles a conjecture raised by Pavez-Signé (2023) in a stronger form.</p></div>\",\"PeriodicalId\":50490,\"journal\":{\"name\":\"European Journal of Combinatorics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001446/pdfft?md5=53af666a1aa86ffe42f097ee615130a5&pid=1-s2.0-S0195669824001446-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0195669824001446\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0195669824001446","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们证明，最小半度至少为 12+ɛn 且 n≥Cm 的 n 个顶点数图 D 包含所有无孤立顶点的 m 弧数图的细分。这里，C 是一个常数，只取决于 ɛ。这是可能的最佳结果，并以更强的形式解决了 Pavez-Signé (2023) 提出的猜想。
We prove that an -vertex digraph with minimum semi-degree at least and contains a subdivision of all -arc digraphs without isolated vertices. Here, is a constant only depending on This is the best possible and settles a conjecture raised by Pavez-Signé (2023) in a stronger form.
期刊介绍：
The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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