报告学者：李佳傲 教授

报告者单位：南开大学

报告时间：2024年7月12日（周五）上午9:30--10:30

报告地点：学活会议室

报告摘要：A signed graph is a graph in which each edge receives a positive or a negative sign. In a signed graph, a sign circuit is either a balanced circuit or a barbell. A signed graph is called flow-admissible if each edge lies in a sign circuit. In this talk, we shall discuss circuit k-cover and shortest circuit cover problems of signed graphs. Motived by Prof. Fan’s classical 6-cover theorem of graphs, we use some flow cover/decomposition techniques to study the circuit cover problem of signed graphs. We show that the circuit cover problem of signed graphs can be reduced to the cubic case in some sense, i.e., if for every cubic graph G, the signed graph (G, -) admits a circuit k-cover, then we can obtain circuit 12k-covers for all flow-admissible signed graphs. Moreover, we show that every flow-admissible signed planar graph admits a circuit 12-cover, whose proof utilizes the 4CT. Using similar ideas, we also connect this problem to the Berge-Fulkerson Conjecture of cubic graphs. 

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，简介：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。