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Judicious partitions of weighted hypergraphs
Xu Xin; Yan GuiYing; Zhang Yao
AbstractLet G be a weighted hypergraph with edges of size i for i = 1, 2. Let wi denote the total weight of edges of size i and a be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollobas and Scott: Does there exist a bipartition such that each class meets edges of total weight at least \ ? We provide an optimal bound for balanced bipartition of weighted hypergraphs, partially establishing this conjecture. For dense graphs, we also give a result for partitions into more than two classes. In particular, it is shown that any graph G with m edges has a partition V-1,...,V (k) such that each vertex set meets at least edges, which answers a related question of Bollobas and Scott.
Keywordjudicious partition balanced bipartition weighted hypergraph
Funding ProjectNational Natural Science Foundation of China[11371355] ; National Natural Science Foundation of China[11471193]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000369948900014
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Document Type期刊论文
Corresponding AuthorYan GuiYing
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Xu Xin,Yan GuiYing,Zhang Yao. Judicious partitions of weighted hypergraphs[J]. SCIENCE CHINA-MATHEMATICS,2016,59(3):609-616.
APA Xu Xin,Yan GuiYing,&Zhang Yao.(2016).Judicious partitions of weighted hypergraphs.SCIENCE CHINA-MATHEMATICS,59(3),609-616.
MLA Xu Xin,et al."Judicious partitions of weighted hypergraphs".SCIENCE CHINA-MATHEMATICS 59.3(2016):609-616.
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