白淑亮

韩苗苗

2026年10月12日 14:30 至 15:30

Online

Tencent 482 969 7386 (106457)

For a finite abelian group $A$, we study the function $c(A)$, defined as the minimum positive integer $k$ such that every flow-admissible $k$-edge-connected signed graph admits a nowhere-zero $A$-flow. We determine $c(A)$ for all finite abelian groups $A$ except $\mathbb{Z}_3$, $\mathbb{Z}_7$, and $\mathbb{Z}_8$, for which we obtain bounds. Our results prove that, for $A= \mathbb{Z}_2^m$ or $\mathbb{Z}_2^n\times \mathbb{Z}_4$ for some $m\ge 3$ or $n\ge 1$, every flow-admissible $2$-edge-connected signed graph admits a nowhere-zero $A$-flow, where the edge connectivity condition is best possible; for all other $A$ of order at least $9$, every flow-admissible signed graph admits a nowhere-zero $A$-flow.

韩苗苗，硕士生导师。主要研究兴趣包括图的染色，Tutte整数流理论等问题，在图论领域J. Combin. Theory Ser. B, SIAM J. Discrete Math, J. Graph Theory 等杂志发表学术论文二十余篇。