{"title":"On Dyadic Fractional Packings of $T$-Joins","authors":"Ahmad Abdi, G. Cornuéjols, Zuzanna Palion","doi":"10.1137/21m1445260","DOIUrl":null,"url":null,"abstract":"Let G = (V,E) be a graph, and T ⊆ V a nonempty subset of even cardinality. The famous theorem of Edmonds and Johnson on the T -join polyhedron implies that the minimum cardinality of a T -cut is equal to the maximum value of a fractional packing of T -joins. In this paper, we prove that the fractions assigned may be picked as dyadic rationals, i.e. of the form a 2k for some integers a, k ≥ 0.","PeriodicalId":21749,"journal":{"name":"SIAM J. Discret. Math.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM J. Discret. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/21m1445260","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
Let G = (V,E) be a graph, and T ⊆ V a nonempty subset of even cardinality. The famous theorem of Edmonds and Johnson on the T -join polyhedron implies that the minimum cardinality of a T -cut is equal to the maximum value of a fractional packing of T -joins. In this paper, we prove that the fractions assigned may be picked as dyadic rationals, i.e. of the form a 2k for some integers a, k ≥ 0.
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