{"title":"四色问题的数值计算","authors":"Oystein Ore, Joel Stemple","doi":"10.1016/S0021-9800(70)80009-6","DOIUrl":null,"url":null,"abstract":"<div><p>It is shown in this paper that a map not colorable in four colors must have at least <em>n</em>=40 countries. This improves on the result <em>n</em>=36 due to C. E. Winn (1940). The rather elaborate computations are based upon the Euler contributions of the faces in an irreducible graph and upon several new reducible configurations.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 1","pages":"Pages 65-78"},"PeriodicalIF":0.0000,"publicationDate":"1970-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80009-6","citationCount":"21","resultStr":"{\"title\":\"Numerical calculations on the four-color problem\",\"authors\":\"Oystein Ore, Joel Stemple\",\"doi\":\"10.1016/S0021-9800(70)80009-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>It is shown in this paper that a map not colorable in four colors must have at least <em>n</em>=40 countries. This improves on the result <em>n</em>=36 due to C. E. Winn (1940). The rather elaborate computations are based upon the Euler contributions of the faces in an irreducible graph and upon several new reducible configurations.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 1\",\"pages\":\"Pages 65-78\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80009-6\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800096\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021980070800096","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 21
摘要
本文证明了不能用四种颜色着色的地图必须至少有n=40个国家。这改进了C. E. Winn(1940)的结果n=36。相当复杂的计算是基于欧拉贡献的面在一个不可约的图和几个新的可约构型。
It is shown in this paper that a map not colorable in four colors must have at least n=40 countries. This improves on the result n=36 due to C. E. Winn (1940). The rather elaborate computations are based upon the Euler contributions of the faces in an irreducible graph and upon several new reducible configurations.
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