{"title":"Solution of the heawood map-coloring problem—Case 2","authors":"Gerhard Ringel , J.W.T. Youngs","doi":"10.1016/S0021-9800(69)80061-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><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 is congruent to 2 modulo 12.</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"7 4","pages":"Pages 342-352"},"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)80061-X","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Combinatorial Theory","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002198006980061X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
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 2 modulo 12.
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