Let 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 α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bol...Let 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 α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/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 Bollobás and Scott.展开更多
基金National Natural Science Foundation of China (Grant Nos. 11371355 and 11471193)
文摘Let 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 α be the maximum weight of an edge of size 1. We study the following partitioning problem of Bollob′as and Scott： Does there exist a bipartition such that each class meets edges of total weight at least （w_1-α）/2＋（2w_2）/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 Bollobás and Scott.
