二因子图和哈密顿图在必要条件下的禁止对

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Qiang Wang , Liming Xiong
{"title":"二因子图和哈密顿图在必要条件下的禁止对","authors":"Qiang Wang ,&nbsp;Liming Xiong","doi":"10.1016/j.dam.2025.05.017","DOIUrl":null,"url":null,"abstract":"<div><div>In <span><span>[1]</span></span>, Wang and Xiong characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that 2-connected <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> who has an even-factor is hamiltonian.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"373 ","pages":"Pages 290-300"},"PeriodicalIF":1.0000,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Forbidden pairs for 2-factorable and hamiltonian graphs under the necessary condition\",\"authors\":\"Qiang Wang ,&nbsp;Liming Xiong\",\"doi\":\"10.1016/j.dam.2025.05.017\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In <span><span>[1]</span></span>, Wang and Xiong characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that 2-connected <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs <span><math><mrow><mi>R</mi><mo>,</mo><mi>S</mi></mrow></math></span> such that connected (or 2-edge-connected) <span><math><mrow><mo>{</mo><mi>R</mi><mo>,</mo><mi>S</mi><mo>}</mo></mrow></math></span>-free graph <span><math><mi>G</mi></math></span> who has an even-factor is hamiltonian.</div></div>\",\"PeriodicalId\":50573,\"journal\":{\"name\":\"Discrete Applied Mathematics\",\"volume\":\"373 \",\"pages\":\"Pages 290-300\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2025-05-15\",\"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/S0166218X25002641\",\"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/S0166218X25002641","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

在[1]中,Wang和Xiong刻画了所有禁止对(非必要连通)R,S,使得含2因子的2连通{R,S}自由图G是哈密顿的。更全面地说,本文刻画了所有禁止对(不一定连通的)R,S,使得连通(或2边连通){R,S}自由图G承认一个2因子是哈密顿的。此外,我们刻画了所有禁止对(非必要连通)R,S,使得连通(或2边连通){R,S}自由图G承认偶因子具有2因子。与Yang and Xiong(2023)的主要结果相比,我们给出了所有断开的禁止对。最后,我们找到了所有的禁止对R,S,使得有偶数因子的连通(或2边连通){R,S}自由图G是哈密顿的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Forbidden pairs for 2-factorable and hamiltonian graphs under the necessary condition
In [1], Wang and Xiong characterize all forbidden pairs (not necessary connected) R,S such that 2-connected {R,S}-free graph G admitting a 2-factor is hamiltonian. To be more comprehensive, in this paper, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting a 2-factor is hamiltonian. Besides, we characterize all forbidden pairs (not necessary connected) R,S such that connected (or 2-edge-connected) {R,S}-free graph G admitting an even-factor has a 2-factor. Comparing with the main result of Yang and Xiong (2023), we give all disconnected forbidden pairs. In the end, we find all forbidden pairs R,S such that connected (or 2-edge-connected) {R,S}-free graph G who has an even-factor is hamiltonian.
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
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信