{"title":"Degree sum condition for vertex-disjoint triangles and pentagons","authors":"Maoqun Wang , Sitong Guan , Bo Zhang","doi":"10.1016/j.dam.2025.02.046","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>n</mi></math></span>, <span><math><mi>r</mi></math></span> and <span><math><mi>s</mi></math></span> be three integers and <span><math><mi>G</mi></math></span> a graph with <span><math><mrow><mi>n</mi><mo>=</mo><mn>3</mn><mi>r</mi><mo>+</mo><mn>5</mn><mi>s</mi></mrow></math></span> vertices. Bauer and Wang proved that if <span><math><mrow><mi>r</mi><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>≥</mo><mn>2</mn><mi>r</mi><mo>+</mo><mn>3</mn><mi>s</mi></mrow></math></span>, then <span><math><mi>G</mi></math></span> contains <span><math><mrow><mi>r</mi><mo>+</mo><mi>s</mi></mrow></math></span> vertex disjoint cycles such that <span><math><mi>r</mi></math></span> of them are triangles and <span><math><mi>s</mi></math></span> of them are pentagons. In 2018, Chiba and Yamashita asked whether the degree condition can be replaced by the degree sum condition. In this paper, we give a positive answer to this question.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"369 ","pages":"Pages 88-95"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-09","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/S0166218X25001180","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
Let , and be three integers and a graph with vertices. Bauer and Wang proved that if , and , then contains vertex disjoint cycles such that of them are triangles and of them are pentagons. In 2018, Chiba and Yamashita asked whether the degree condition can be replaced by the degree sum condition. In this paper, we give a positive answer to this question.
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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