关于举行李佳傲教授（南开大学）学术报告会的通知

报告主题:    On flows and group connectivity of graphs

报  告  人:    李佳傲教授

报告时间:    2024年 5月19日（星期日）上午10：00-11：00

报告地点:    腾讯会议：660-873-541

邀  请  人:    林鸿莺副教授

欢迎广大师生前往！

数学学院

2024年5月9日

报告摘要：The equivalence of group connectivity for non-homogeneous groups with the same order has been concerned since Jaeger, Linial, Payan and Tarsi introduced this concept in [J. Combin. Theory Ser. B, 56 (1992) 165-182]. Hušek, Mohelníková and Šámal in [J. Graph Theory, 93 (2020) 317-327] showed that Z₄-connectivity and Z₂²-connectivity are not equivalent by finding counterexamples with a computer-assisted proof, and they asked whether one can find a proof that does not use computers. Langhede and Thomassen [European J. Combin., (2023) 103816] provided a compute-free proof to show that there exist 3-edge-connected and Z₂²-connected, but not Z₄-connected graphs. In this talk, we construct 3-edge-connected graphs which are Z₄-connected but not Z₂²-connected in which we prove those properties without any involvement of computers. These two results together answer the question proposed by Hu\v{s}ek et al. about computer-free proofs on the non-equivalence of Z₄-connectivity and Z₂²-connectivity. In addition, by using both theoretical reductions and computer searching we find the smallest graph whose Z₄-connectivity varies from Z₂²-connectivity. This smallest graph (in terms of order and size) is unique, which has 10 vertices and 14 edges.

报告人介绍：李佳傲，南开大学数学科学学院，教授，博士生导师。本科和硕士毕业于中国科学技术大学，博士毕业于美国西弗吉尼亚大学（导师为赖虹建教授）。之后入职南开大学，历任讲师、副教授，2022年12月至今任教授。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，加性组合，网络与组合优化等问题。已完成和发表论文三十余篇，研究成果发表在J. Combin. Theory Ser. B, SIAM J. Discrete Math, J. Graph Theory 等杂志。担任天津市数学会秘书长，中国运筹学会图论组合分会理事，以及SCI杂志Journal of Combinatorial Optimization的副编辑（Associate Editor）等学术兼职。入选天津市“131”创新型人才培养工程第三层次(2019)，天津市青年人才托举工程(2020)，南开大学百名青年学科带头人培养计划(2021)。2022年获国家自然科学基金优秀青年科学基金项目资助。