On group connectivity of graphs
数学专题报告
报告题目(Title)：On group connectivity of graphs
报告人(Speaker)：李佳傲教授 （南开大学）
地点(Place)：2024 年 7 月 12 日（周五） 14:50--15:50
时间(Time)：后主楼1220
邀请人(Inviter)：徐敏
报告摘要
The equivalence of group connectivity for non-homogeneous groups with a same order has been concerned since Jaeger, Linial, Payan and Tarsi introduced this concept in [J. Combin. Theory Ser. B, 56 (1992) 165-182]. With a computer-assisted proof, Hu\v{s}ek, Moheln\'{i}kov\'{a} and \v{S}\'{a}mal in [J. Graph Theory, 93 (2020) 317-327] showed that $\Z_4$-connectivity and $\Z_2^2$-connectivity are not equivalent by finding counterexamples. In this talk, by using both theoretical reductions and computer searching, we find the smallest graph whose $\Z_4$-connectivity varies from $\Z_2^2$-connectivity. This smallest graph (in terms of order and size) is unique, which has $10$ vertices and $14$ edges. Furthermore, we construct $3$-edge-connected graphs which are $\Z_4$-connected but not $\Z_2^2$-connected in which we prove those properties without any involvement of computers. Note that Langhede and Thomassen (European J. Combin., (2023) 103816) provide a compute-free proof to show that there exist $3$-edge-connected $\Z_2^2$- and non-$\Z_4$-connected planar graphs. These two results together completely answer the question proposed by Hu\v{s}ek et al.(JGT2020) about computer-free proofs on the non-equivalence of $\Z_4$-connectivity and $\Z_2^2$-connectivity.
主讲人简介
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）。2022年12月至今任南开大学数学科学学院教授。主要研究兴趣是离散数学与组合图论。包括图的染色，Tutte整数流理论，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。
