{"title":"$T$-连接的并进分数填充","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":"20 1","pages":"2445-2451"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"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\":\"20 1\",\"pages\":\"2445-2451\"},\"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}","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}
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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