{"title":"On the Boolean dimension of a graph and other related parameters","authors":"M. Pouzet, H. S. Kaddour, Bhalchandra D. Thatte","doi":"10.46298/dmtcs.7437","DOIUrl":null,"url":null,"abstract":"We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the Boolean dimension with the inversion index of a tournament.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"96 3 Pt 1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discret. Math. Theor. Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/dmtcs.7437","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
We present the Boolean dimension of a graph, we relate it with the notions of inner, geometric and symplectic dimensions, and with the rank and minrank of a graph. We obtain an exact formula for the Boolean dimension of a tree in terms of a certain star decomposition. We relate the Boolean dimension with the inversion index of a tournament.
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