{"title":"Structure of (bull, diamond)-free graphs and its applications","authors":"Suchismita Mishra","doi":"10.1016/j.dam.2025.02.026","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we discuss the complete structure of the (bull, diamond)-free graphs. As an application of that, we give the characterization of the partitionable (bull, diamond)-free graphs. Moreover, we show that such a partition for a partitionable (bull, diamond)-free graph can be found in polynomial time. Additionally, we show that the cop number of a (bull, diamond)-free graph containing a triangle is at most two less than its diameter. Furthermore, the cop number of a connected (<span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, bull, diamond)-free graph with a triangle, is at most <span><math><mrow><mi>n</mi><mo>−</mo><mn>3</mn></mrow></math></span>, for any natural number <span><math><mrow><mi>n</mi><mo>></mo><mn>3</mn></mrow></math></span>. We also discuss a couple of applications of the structural theorem of the (bull, diamond)-free graphs in the conclusions.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"368 ","pages":"Pages 176-183"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-04","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/S0166218X25000952","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
Abstract
In this paper, we discuss the complete structure of the (bull, diamond)-free graphs. As an application of that, we give the characterization of the partitionable (bull, diamond)-free graphs. Moreover, we show that such a partition for a partitionable (bull, diamond)-free graph can be found in polynomial time. Additionally, we show that the cop number of a (bull, diamond)-free graph containing a triangle is at most two less than its diameter. Furthermore, the cop number of a connected (, bull, diamond)-free graph with a triangle, is at most , for any natural number . We also discuss a couple of applications of the structural theorem of the (bull, diamond)-free graphs in the conclusions.
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.