 # HOẠT ĐỘNG TRONG TUẦN

A decomposition for digraphs of minimum outdegree 3 without vertex disjoint directed cycles of different lengths (phần 2).
 Báo cáo viên: Ngô Đắc TânThời gian: 9h30, thứ 5, ngày 13/12/2018Địa điểm: Phòng 611- 612, nhà A6, Viện Toán học, 18 Hoàng Quốc Việt.Tóm tắt: We prove that a digraph \$D=(V,A)\$ of minimum outdegree 3 without vertex disjoint directed cycles of different lengths is a union of three digraphs \$D_1=(V_1,A_1), D_2=(V_2,A_2)\$ and \$D_3=(V_3,A_3)\$ such that \$V=V_1cup V_2\$, where \$V_1cap V_2=emptyset\$, \$V_2eemptyset\$ but \$V_1\$ may be empty, \$D_1\$ is the subdigraph of \$D\$ induced by \$V_1\$ and is an acyclic digraph, \$D_2\$ is the subdigraph of \$D\$ induced by \$V_2\$ and is a strong digraph of minimum outdegree 3 without vertex disjoint directed cycles of different lengths, \$D_3\$ is a subdigraph of \$D\$ every arc of which has its tail in \$V_1\$ and its head in \$V_2\$ and for every vertex \$vin V_1\$, \$d^+_{D_1cup D_3}(v)ge 3\$. Moreover, such a decomposition of \$D\$ is unique. Further, we show that .the converse of the above decomposition is also true. For the case of girth 2, we get a classification for such digraphs

### Tin tức nổi bật

 29/06/21, Hội nghị, hội thảo:The 7th International Conference on Random Dynamical Systems