Nowhere-zero 3-flows in toroidal graphs

活动时间： 04月22日16时00分       

地            点  ： 腾讯会议：495 985 806

讲座内容：

A nowhere-zero 3-flow of a graph G is anorientation together with a mapping from $E(G)$ to $\{1,2\}$ such that thenet-outflow equals net-inflow at every vertex. Tutte's 3-flow conjecture from1972 states that every 4-edge-connected graph admits a nowhere-zero 3-flow. Theplanar case of Tutte's 3-flow conjecture is the classical Grotzsch's Theorem obtainedin 1958. Steinberg and Younger in 1989 further verified Tutte's 3-flowconjecture for projective planar graphs. In this talk, we confirm Tutte's3-flow conjecture for all toroidal graphs, resolving a question of Steinberg[The state of three color problem, Annals of Discrete Mathematics, 1993]. Themajor step is to address 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-zero3-flow. This paper is recently published in [Journal of Combinatorial Theory,Series B, 153 (2022) 61-80].

主讲人介绍：

李佳傲，南开大学数学科学学院副教授，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二十余篇。现主持国家自然科学基金青年项目1项，天津市基金2项。

发布时间：2022-04-20 09:50:04