{"title":"1 平面图形中的等价着色","authors":"Daniel W. Cranston, Reem Mahmoud","doi":"10.1016/j.disc.2024.114286","DOIUrl":null,"url":null,"abstract":"<div><div>For every <span><math><mi>r</mi><mo>≥</mo><mn>13</mn></math></span>, we show every 1-planar graph <em>G</em> with <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>r</mi></math></span> has an equitable <em>r</em>-coloring.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 2","pages":"Article 114286"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Equitable coloring in 1-planar graphs\",\"authors\":\"Daniel W. Cranston, Reem Mahmoud\",\"doi\":\"10.1016/j.disc.2024.114286\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For every <span><math><mi>r</mi><mo>≥</mo><mn>13</mn></math></span>, we show every 1-planar graph <em>G</em> with <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mi>r</mi></math></span> has an equitable <em>r</em>-coloring.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 2\",\"pages\":\"Article 114286\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-10-18\",\"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/S0012365X24004175\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"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/S0012365X24004175","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
对于每一个 r≥13，我们都能证明Δ(G)≤r 的每一个 1 平面图形 G 都有一个公平的 r 着色。
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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