{"title":"heawood地图上色问题的解法——案例8","authors":"Gerhard Ringel , J.W.T. Youngs","doi":"10.1016/S0021-9800(69)80062-1","DOIUrl":null,"url":null,"abstract":"<div><p>This paper gives a proof of the fact that the chromatic number of an orientable surface of genus <em>p</em> is equal to the integral part of <span><math><mrow><mo>(</mo><mn>7</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>48</mn><mi>p</mi><mo>)</mo></mrow></msqrt><mo>/</mo><mn>2</mn></mrow></math></span> whenever the latter s congruent to 8 modulo 12.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"7 4","pages":"Pages 353-363"},"PeriodicalIF":0.0000,"publicationDate":"1969-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(69)80062-1","citationCount":"8","resultStr":"{\"title\":\"Solution of the heawood map-coloring problem—Case 8\",\"authors\":\"Gerhard Ringel , J.W.T. Youngs\",\"doi\":\"10.1016/S0021-9800(69)80062-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper gives a proof of the fact that the chromatic number of an orientable surface of genus <em>p</em> is equal to the integral part of <span><math><mrow><mo>(</mo><mn>7</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>48</mn><mi>p</mi><mo>)</mo></mrow></msqrt><mo>/</mo><mn>2</mn></mrow></math></span> whenever the latter s congruent to 8 modulo 12.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"7 4\",\"pages\":\"Pages 353-363\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1969-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(69)80062-1\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980069800621\",\"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/S0021980069800621","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solution of the heawood map-coloring problem—Case 8
This paper gives a proof of the fact that the chromatic number of an orientable surface of genus p is equal to the integral part of whenever the latter s congruent to 8 modulo 12.
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