无（牛，菱形）图的结构及其应用

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-03-04 DOI:10.1016/j.dam.2025.02.026

Suchismita Mishra

{"title":"无（牛，菱形）图的结构及其应用","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":"{\"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}","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

摘要

本文讨论了无（牛，菱形）图的完备结构。作为该方法的一个应用，我们给出了可分割（牛，菱形）自由图的表征。此外，我们证明了可分（牛，菱形）自由图的这种划分可以在多项式时间内找到。此外，我们证明了包含三角形的（牛，菱形）自由图的cop数最多比其直径小2。更进一步，对于任意自然数n>；3，具有三角形的连通（Pn，牛，菱形）自由图的cop数最多为n−3。在结论部分还讨论了无（牛，菱形）图结构定理的几个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Structure of (bull, diamond)-free graphs and its applications

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 (

P_{n}

, bull, diamond)-free graph with a triangle, is at most

n - 3

, for any natural number

n > 3

. We also discuss a couple of applications of the structural theorem of the (bull, diamond)-free graphs in the conclusions.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

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.