报告题目：Flows and Homomorphisms of Planar Graphs

报告简介：It was conjectured by Jaeger that every planar graph of girth $4t$ has a homomorphism to the odd cycle of length $2t+1$. By duality, this can be modified to a more general Planar Circular Flow Conjecture: Every $2k$-edge-connected planar graph admits a circular $(2+2/k)$-flow. The $k=1,2$ cases are known as the 4CT and Grotzsch's theorem(3CT). It is open for $k\ge 3$. In this talk, we make further progress on the cases of $k=4,6$ by showing the following: (i) every $10$-edge-connected planar graph admits a circular $5/2$-flow, and (ii) every $16$-edge-connected planar graph admits a circular $7/3$-flow.

Note that the dual version of statement (i) on homomorphism was previously proved by Dvorak-Postle (Combinatorica 2017) with a compute-aided proof, while our argument is compute-free and much shorter with additional implication on antisymmetric flows. The dual of statement (ii) indicates that every planar graph of girth $16$ has a homomorphism to the 7-cycle.

报告人：李佳傲，南开大学数学科学学院硕士生导师。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。

报告时间：2021年1月27日（星期三）下午 3:30-5:00.

报告地点：腾讯会议，ID：733 669 976

主办单位：扬州大学数学科学学院

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