{"title":"最大度不超过5的平面图的2-距离16着色","authors":"Zakir Deniz","doi":"10.1016/j.disc.2024.114379","DOIUrl":null,"url":null,"abstract":"<div><div>A vertex coloring of a graph <em>G</em> is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that <em>G</em> is a planar graph with a maximum degree at most 5. We prove that <em>G</em> admits a 2-distance 16-coloring, which improves the result given by Zou et al. (2024) <span><span>[13]</span></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 4","pages":"Article 114379"},"PeriodicalIF":1.1000,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On 2-distance 16-coloring of planar graphs with maximum degree at most five\",\"authors\":\"Zakir Deniz\",\"doi\":\"10.1016/j.disc.2024.114379\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>A vertex coloring of a graph <em>G</em> is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that <em>G</em> is a planar graph with a maximum degree at most 5. We prove that <em>G</em> admits a 2-distance 16-coloring, which improves the result given by Zou et al. (2024) <span><span>[13]</span></span>.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 4\",\"pages\":\"Article 114379\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2025-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X24005107\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/12/30 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24005107","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/30 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
如果任意两个相距不超过2的顶点得到不同的颜色，则图G的顶点着色称为2距离着色。设G是一个最大度数不超过5的平面图。我们证明了G允许2距离16着色，改进了Zou et al.(2024)[13]给出的结果。
On 2-distance 16-coloring of planar graphs with maximum degree at most five
A vertex coloring of a graph G is called a 2-distance coloring if any two vertices at a distance at most 2 from each other receive different colors. Suppose that G is a planar graph with a maximum degree at most 5. We prove that G admits a 2-distance 16-coloring, which improves the result given by Zou et al. (2024) [13].
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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