{"title":"列表4平面图的颜色","authors":"Xuding Zhu","doi":"10.1016/j.jctb.2023.04.001","DOIUrl":null,"url":null,"abstract":"<div><p>This paper proves the following result: If <em>G</em><span> is a planar graph and </span><em>L</em> is a 4-list assignment of <em>G</em> such that <span><math><mo>|</mo><mi>L</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>∩</mo><mi>L</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>|</mo><mo>≤</mo><mn>2</mn></math></span> for every edge <em>xy</em>, then <em>G</em> is <em>L</em>-colourable. This answers a question asked by Kratochvíl et al. (1998) <span>[10]</span>.</p></div>","PeriodicalId":54865,"journal":{"name":"Journal of Combinatorial Theory Series B","volume":"162 ","pages":"Pages 1-12"},"PeriodicalIF":1.3000,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"List 4-colouring of planar graphs\",\"authors\":\"Xuding Zhu\",\"doi\":\"10.1016/j.jctb.2023.04.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper proves the following result: If <em>G</em><span> is a planar graph and </span><em>L</em> is a 4-list assignment of <em>G</em> such that <span><math><mo>|</mo><mi>L</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>∩</mo><mi>L</mi><mo>(</mo><mi>y</mi><mo>)</mo><mo>|</mo><mo>≤</mo><mn>2</mn></math></span> for every edge <em>xy</em>, then <em>G</em> is <em>L</em>-colourable. This answers a question asked by Kratochvíl et al. (1998) <span>[10]</span>.</p></div>\",\"PeriodicalId\":54865,\"journal\":{\"name\":\"Journal of Combinatorial Theory Series B\",\"volume\":\"162 \",\"pages\":\"Pages 1-12\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory Series B\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0095895623000291\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/4/20 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory Series B","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0095895623000291","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/4/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
This paper proves the following result: If G is a planar graph and L is a 4-list assignment of G such that for every edge xy, then G is L-colourable. This answers a question asked by Kratochvíl et al. (1998) [10].
期刊介绍：
The Journal of Combinatorial Theory publishes original mathematical research dealing with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series B is concerned primarily with graph theory and matroid theory and is a valuable tool for mathematicians and computer scientists.
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