12月6日 李佳傲博士学术报告（数统学院）

报 告 人：李佳傲 博士

报告题目：Modulo Orientation of Graphs

报告时间：2016年12月6日 15:30

报告地点：静远楼1506报告厅

主办单位：数学与统计学院、科技处

报告摘要：

　　A modulo $(2p+1)$-orientation $D$ is an orientation of $G$ such

that the indegree is congruent to outdegree modulo $(2p+1)$ for every vertex of $G$. Jaeger conjectured that every $4p$-edge-connected graph admits a modulo

$(2p+1)$-orientation. The $p=1$ case is equivalent to Tutte's $3$-Flow Conjecture, and the case of $p=2$, if true, would imply Tutte's $5$-Flow Conjecture. In this talk, we introduce some known results and discuss new results on modulo $(2p+1)$-orientation and its contractible configurations. We show that if a family of graphs has bounded independence number, then there are only finite many contraction obstacles for admitting modulo $(2p+1)$-orientations. Applying this to verify certain small contraction obstacles, in particular, we show every $4$-edge-connected graph with independence number at most $4$ admits a modulo $3$-orientation.

报告人简介：

　　李佳傲，毕业于中国科学技术大学，现为美国西弗吉尼亚大学博士，师从赖虹建教授。主要研究离散数学与组合图论。在图的整数流理论和相关问题中有深入研究，取得多项成果，完成和发表了多篇关于Tutte的整数流猜想相关的论文。