报告名称：Nowhere-zero 3-flows in toroidal graphs

主办单位：数学与统计学学院

报告专家：李佳傲

专家所在单位：南开大学

报告时间：2021年1月14日14：00

报告地点：腾讯会议（会议ID：799 344 206）

专家简介：李佳傲，南开大学数学科学学院讲师，硕士生导师。2012年和2014年在中国科学技术大学获得本科和硕士学位。2018年博士毕业于美国西弗吉尼亚大学，导师为赖虹建教授。2018年7月入职南开大学数学科学学院。主要研究兴趣是离散数学与组合图论。包括Tutte整数流理论,图的染色，图结构与分解，网络与组合优化等问题。已在本专业主流杂志发表论文近二十篇。现主持国家自然科学基金青年项目1项，天津市基金2项。

报告摘要：A nowhere-zero 3-flow of a graph G is an orientation together with a mapping from $E(G)$ to $\{1,2\}$ such that the net-outflow equals net-inflow at every vertex. Tutte's 3-flow conjecture from 1972 states that every 4-edge-connected graph admits a nowhere-zero 3-flow. The planar case of Tutte's 3-flow conjecture is the classical Grotzsch's Theorem obtained in 1958. Steinberg and Younger in 1989 further verified Tutte's 3-flow conjecture for projective planar graphs. In this talk, we confirm Tutte's 3-flow conjecture for all toroidal graphs, resolving a question of Steinberg [The state of three color problem, Annals of Discrete Mathematics, 1993]. The major step is to answer a question of Thomassen in 1993 (in Jensen-Toft book ``Graph coloring problems''), showing that if a 4-edge-connected graph $G$ contains an edge $e$ such that $G-e$ is planar, then $G$ admits a nowhere-zero 3-flow.

邀请人：刘慧清