{"title":"矩阵的双着色与公平双着色","authors":"M. Conforti, G. Cornuéjols, G. Zambelli","doi":"10.1137/1.9780898718805.ch4","DOIUrl":null,"url":null,"abstract":"Two classical theorems of Ghouila-Houri and Berge characterize total unimodularity and balancedness in terms of equitable bicolorings and bicolorings, respectively. In this paper, we prove a bicoloring result that provides a common generalization of these two theorems.","PeriodicalId":416196,"journal":{"name":"The Sharpest Cut","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bicolorings and Equitable Bicolorings of Matrices\",\"authors\":\"M. Conforti, G. Cornuéjols, G. Zambelli\",\"doi\":\"10.1137/1.9780898718805.ch4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two classical theorems of Ghouila-Houri and Berge characterize total unimodularity and balancedness in terms of equitable bicolorings and bicolorings, respectively. In this paper, we prove a bicoloring result that provides a common generalization of these two theorems.\",\"PeriodicalId\":416196,\"journal\":{\"name\":\"The Sharpest Cut\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Sharpest Cut\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/1.9780898718805.ch4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Sharpest Cut","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/1.9780898718805.ch4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Two classical theorems of Ghouila-Houri and Berge characterize total unimodularity and balancedness in terms of equitable bicolorings and bicolorings, respectively. In this paper, we prove a bicoloring result that provides a common generalization of these two theorems.
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