报告名称：Converting modular flows to integer flows in signed graphs

报告专家：李佳傲

专家所在单位：南开大学

报告时间：2023年11月30日

报告地点: 英国威廉希尔体育公司201

专家简介：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。

报告摘要：The concept of flows on signed graphs naturally comes from the dual of local tensions of graphs embedded on non-orientable surfaces. It was conjectured by Bouchet in 1983 that every flow-admissible signed graph admits a nowhere-zero integer 6-flow. The recent 11-flow theorem of signed graphs, obtained by us in JCTB2021, is established by proving the existence of a balanced $Z_2\times Z_3$-flow, and then converting $Z_2$-, $Z_3$-flows to integer 3-, 5-flows, respectively. It is crucial to study on how to convert $Z_k$-flows to better integer flows. In this talk, we will show that every bridgeless signed graph with a nowhere-zero $Z_5$-flow admits a nowhere-zero integer 7-flow. The key steps in the proof are some reduction techniques introduced in our recent work (SIAMDM 2021) and some tools from graph factors.