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| 1 | 图的划分:一些进展与未解决问题(英文)显示文摘图的划分问题是图论研究中最重要的一个问题之一,图论研究的很多问题都是特殊形式的划分问题,比如经典染色理论要求将图划分成最少的独立集,而最大尼-部子图问题则是要找图中边数最多的一个k-部子图.本文给出划分问题的一些最新进展,以及一些尚未解决的问题,其中大部分是来自于求最大k-部子图的相关领域. | 许宝刚 | 2016 | 数学进展2016，45，1： | 8 |
| 2 | A bound on judicious bipartitions of directed graphs显示文摘Judicious partitioning problems on graphs ask for partitions that bound several quantities simultaneously,which have received much attention lately.Scott(2005)asked the following natural question:What is the maximum constant cdsuch that every directed graph D with m arcs and minimum outdegree d admits a bipartition V(D)=V_1∪V_2 satisfying min{e(V_1,V_2),e(V_2,V_1)}cdm?Here,for i=1,2,e(V_i,V_(3-i))denotes the number of arcs in D from V_i to V_(3-i).Lee et al.(2016)conjectured that every directed graph D with m arcs and minimum outdegree at least d 2 admits a bipartition V(D)=V_1∪V_2 such that min{e(V_1,V_2),e(V_2,V_1)}≥((d-1)/(2(2 d-1))+o(1))m.In this paper,we show that this conjecture holds under the additional natural condition that the minimum indegree is also at least d. | Jianfeng Hou Huawen Ma Xingxing Yu Xia Zhang | 2020 | Science China Mathematics2020，63，2： | 0 |
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