{"title":"截线和矩阵划分","authors":"J. Edmonds, D. R. Fulkerson","doi":"10.6028/JRES.069B.016","DOIUrl":null,"url":null,"abstract":"Abstract : A matroid M = (E, F) is a finite set E of elements and a family F of subsets of E, called independent sets, such that (1) every subset of an independent set is independent, and (2) for every set A belonging to E, all maximal independent subsets of A have the same cardinality, called the rank r(A) of A. The concept of 'matroid' thus generalizes that of 'matrix' or, in particular, that of 'graph.' This paper treats a variety of partition problems involving independent sets of matroids.","PeriodicalId":408709,"journal":{"name":"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1965-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"251","resultStr":"{\"title\":\"Transversals and Matroid Partition\",\"authors\":\"J. Edmonds, D. R. Fulkerson\",\"doi\":\"10.6028/JRES.069B.016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract : A matroid M = (E, F) is a finite set E of elements and a family F of subsets of E, called independent sets, such that (1) every subset of an independent set is independent, and (2) for every set A belonging to E, all maximal independent subsets of A have the same cardinality, called the rank r(A) of A. The concept of 'matroid' thus generalizes that of 'matrix' or, in particular, that of 'graph.' This paper treats a variety of partition problems involving independent sets of matroids.\",\"PeriodicalId\":408709,\"journal\":{\"name\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1965-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"251\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.6028/JRES.069B.016\",\"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 Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.6028/JRES.069B.016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Abstract : A matroid M = (E, F) is a finite set E of elements and a family F of subsets of E, called independent sets, such that (1) every subset of an independent set is independent, and (2) for every set A belonging to E, all maximal independent subsets of A have the same cardinality, called the rank r(A) of A. The concept of 'matroid' thus generalizes that of 'matrix' or, in particular, that of 'graph.' This paper treats a variety of partition problems involving independent sets of matroids.
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