{"title":"图形具有强奇偶因子的谱条件","authors":"Sizhong Zhou , Tao Zhang , Qiuxiang Bian","doi":"10.1016/j.dam.2024.09.003","DOIUrl":null,"url":null,"abstract":"<div><p>A graph <span><math><mi>G</mi></math></span> has the strong parity property if for every subset <span><math><mrow><mi>X</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mo>|</mo><mi>X</mi><mo>|</mo></mrow></math></span> even, <span><math><mi>G</mi></math></span> has a spanning subgraph <span><math><mi>F</mi></math></span> satisfying <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≡</mo><mn>1</mn></mrow></math></span> (mod 2) for any <span><math><mrow><mi>u</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>≡</mo><mn>0</mn></mrow></math></span> (mod 2) for any <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>∖</mo><mi>X</mi></mrow></math></span>. In this paper, we give a spectral radius condition to guarantee that a connected graph has the strong parity property.</p></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"360 ","pages":"Pages 188-195"},"PeriodicalIF":1.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A spectral condition for a graph to have strong parity factors\",\"authors\":\"Sizhong Zhou , Tao Zhang , Qiuxiang Bian\",\"doi\":\"10.1016/j.dam.2024.09.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A graph <span><math><mi>G</mi></math></span> has the strong parity property if for every subset <span><math><mrow><mi>X</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><mo>|</mo><mi>X</mi><mo>|</mo></mrow></math></span> even, <span><math><mi>G</mi></math></span> has a spanning subgraph <span><math><mi>F</mi></math></span> satisfying <span><math><mrow><mi>δ</mi><mrow><mo>(</mo><mi>F</mi><mo>)</mo></mrow><mo>≥</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>≡</mo><mn>1</mn></mrow></math></span> (mod 2) for any <span><math><mrow><mi>u</mi><mo>∈</mo><mi>X</mi></mrow></math></span>, and <span><math><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>F</mi></mrow></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>≡</mo><mn>0</mn></mrow></math></span> (mod 2) for any <span><math><mrow><mi>v</mi><mo>∈</mo><mi>V</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>∖</mo><mi>X</mi></mrow></math></span>. In this paper, we give a spectral radius condition to guarantee that a connected graph has the strong parity property.</p></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"360 \",\"pages\":\"Pages 188-195\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-09-13\",\"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/S0166218X24003925\",\"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/S0166218X24003925","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A spectral condition for a graph to have strong parity factors
A graph has the strong parity property if for every subset with even, has a spanning subgraph satisfying , (mod 2) for any , and (mod 2) for any . In this paper, we give a spectral radius condition to guarantee that a connected graph has the strong parity property.
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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