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Xu Xin; Yan Guiying; Zhang Yao
Source Publicationsciencechinamathematics
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 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 (w_1–α)/2 + (2w2)/3 ? 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 (1 – (1 – 1/k)~2)m + o(m) edges, which answers a related question of Bollobas and Scott.
Document Type期刊论文
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GB/T 7714
Xu Xin,Yan Guiying,Zhang Yao. csciencechinapressandspringerverlagberlinheidelberg2015mathscichinacomlinkspringercomjudiciouspartitionsofweightedhypergraphs[J]. sciencechinamathematics,2016,59(3):609.
APA Xu Xin,Yan Guiying,&Zhang Yao.(2016).csciencechinapressandspringerverlagberlinheidelberg2015mathscichinacomlinkspringercomjudiciouspartitionsofweightedhypergraphs.sciencechinamathematics,59(3),609.
MLA Xu Xin,et al."csciencechinapressandspringerverlagberlinheidelberg2015mathscichinacomlinkspringercomjudiciouspartitionsofweightedhypergraphs".sciencechinamathematics 59.3(2016):609.
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