{"title":"K5的交叉数n","authors":"Daniel J. Kleitman","doi":"10.1016/S0021-9800(70)80087-4","DOIUrl":null,"url":null,"abstract":"<div><p>Several arguments are presented which provide restrictions on the possible number of crossings in drawings of bipartite graphs. In particular it is shown that <em>cr(K<sub>5,n</sub>)</em>=4[1/2<em>n</em>][1/2(<em>n</em>−1)] and <em>cr(K<sub>6,n</sub>)</em>=6[1/2<em>n</em>][1/2(<em>n</em>−1)].</p></div>","PeriodicalId":100765,"journal":{"name":"Journal of Combinatorial Theory","volume":"9 4","pages":"Pages 315-323"},"PeriodicalIF":0.0000,"publicationDate":"1970-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80087-4","citationCount":"221","resultStr":"{\"title\":\"The crossing number of K5,n\",\"authors\":\"Daniel J. Kleitman\",\"doi\":\"10.1016/S0021-9800(70)80087-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Several arguments are presented which provide restrictions on the possible number of crossings in drawings of bipartite graphs. In particular it is shown that <em>cr(K<sub>5,n</sub>)</em>=4[1/2<em>n</em>][1/2(<em>n</em>−1)] and <em>cr(K<sub>6,n</sub>)</em>=6[1/2<em>n</em>][1/2(<em>n</em>−1)].</p></div>\",\"PeriodicalId\":100765,\"journal\":{\"name\":\"Journal of Combinatorial Theory\",\"volume\":\"9 4\",\"pages\":\"Pages 315-323\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1970-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/S0021-9800(70)80087-4\",\"citationCount\":\"221\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Combinatorial Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021980070800874\",\"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/S0021980070800874","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Several arguments are presented which provide restrictions on the possible number of crossings in drawings of bipartite graphs. In particular it is shown that cr(K5,n)=4[1/2n][1/2(n−1)] and cr(K6,n)=6[1/2n][1/2(n−1)].
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