{"title":"论最小k弧连接数图中缺度为k的顶点","authors":"Jun Fan, Xiaomin Hu, Weihua Yang, Shuang Zhao","doi":"10.1016/j.dam.2024.11.009","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>k</mi></math></span> be a positive integer, and <span><math><mrow><mi>D</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>,</mo><mi>E</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> be a minimally <span><math><mi>k</mi></math></span>-arc-connected simple digraph. Mader conjectured (Combinatorics 2 (1996) 423-449) that there are at least <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices of outdegree <span><math><mi>k</mi></math></span> in <span><math><mi>D</mi></math></span>. In this paper we prove that there are at least four vertices of outdegree <span><math><mi>k</mi></math></span> for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"361 ","pages":"Pages 465-472"},"PeriodicalIF":1.0000,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On vertices of outdegree k in minimally k-arc-connected digraphs\",\"authors\":\"Jun Fan, Xiaomin Hu, Weihua Yang, Shuang Zhao\",\"doi\":\"10.1016/j.dam.2024.11.009\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <span><math><mi>k</mi></math></span> be a positive integer, and <span><math><mrow><mi>D</mi><mo>=</mo><mrow><mo>(</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>,</mo><mi>E</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> be a minimally <span><math><mi>k</mi></math></span>-arc-connected simple digraph. Mader conjectured (Combinatorics 2 (1996) 423-449) that there are at least <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices of outdegree <span><math><mi>k</mi></math></span> in <span><math><mi>D</mi></math></span>. In this paper we prove that there are at least four vertices of outdegree <span><math><mi>k</mi></math></span> for <span><math><mrow><mi>k</mi><mo>≥</mo><mn>3</mn></mrow></math></span>.</div></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"361 \",\"pages\":\"Pages 465-472\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166218X24004827\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X24004827","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
摘要
设 k 为正整数，D=(V(D),E(D)) 为最小 k 弧连接的简单图。Mader 猜想（《组合论》2 (1996) 423-449）D 中至少有 k+1 个缺度为 k 的顶点。
On vertices of outdegree k in minimally k-arc-connected digraphs
Let be a positive integer, and be a minimally -arc-connected simple digraph. Mader conjectured (Combinatorics 2 (1996) 423-449) that there are at least vertices of outdegree in . In this paper we prove that there are at least four vertices of outdegree for .
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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