{"title":"heawood地图上色问题——案例1、7和10","authors":"J.W.T. Youngs","doi":"10.1016/S0021-9800(70)80076-X","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><mrow><mrow><mrow><mo>(</mo><mrow><mn>7</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>48</mn><mi>p</mi></mrow></msqrt></mrow><mo>)</mo></mrow></mrow><mo>/</mo><mn>2</mn></mrow></mrow></math></span> whenever the latter is congruent to 1, 7 or 10 modulo 12.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"8 2","pages":"Pages 220-231"},"PeriodicalIF":0.0000,"publicationDate":"1970-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80076-X","citationCount":"16","resultStr":"{\"title\":\"The heawood map-coloring problem—Cases 1, 7, and 10\",\"authors\":\"J.W.T. Youngs\",\"doi\":\"10.1016/S0021-9800(70)80076-X\",\"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><mrow><mrow><mrow><mo>(</mo><mrow><mn>7</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>48</mn><mi>p</mi></mrow></msqrt></mrow><mo>)</mo></mrow></mrow><mo>/</mo><mn>2</mn></mrow></mrow></math></span> whenever the latter is congruent to 1, 7 or 10 modulo 12.</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"8 2\",\"pages\":\"Pages 220-231\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80076-X\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S002198007080076X\",\"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/S002198007080076X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The heawood map-coloring problem—Cases 1, 7, and 10
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 is congruent to 1, 7 or 10 modulo 12.
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