{"title":"Planar graphs with distance of 3-cycles at least 2 and no cycles of lengths 5, 6, 7","authors":"","doi":"10.1016/j.amc.2024.128946","DOIUrl":null,"url":null,"abstract":"<div><p>Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of 3-cycles at least 2 and no cycles of lengths <span><math><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn></math></span> are weakly 2-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest.</p></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics and Computation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0096300324004077","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Weak degeneracy of a graph is a variation of degeneracy that has a close relationship to many graph coloring parameters. In this article, we prove that planar graphs with distance of 3-cycles at least 2 and no cycles of lengths are weakly 2-degenerate. Furthermore, such graphs can be vertex-partitioned into two subgraphs, one of which has no edges, and the other is a forest.
期刊介绍：
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
