 # WEEKLY ACTIVITIES

On Epidemics Network Model
 Speaker: Le Chi NgocTime: 9h30, Thursday, December 27, 2018Location: Room seminar 6 floor, Building A6, Institute of MathematicsAbstract: 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_2 eemptyset\$ 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.

### Highlights

 31/10/22, Conference:International school on algebraic geometry and algebraic groups 08/08/23, Conference:Đại hội Toán học Việt Nam lần thứ X