报告题目：Circuit Covers of Signed Graphs

报 告 人：李佳傲，南开大学

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.

报告人简介：李佳傲，南开大学数学科学学院副教授、博士生导师。2022年获国家自然科学基金优秀青年科学基金项目资助。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。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)。主要研究兴趣是离散数学与组合图论，已完成和发表论文二十余篇，研究成果发表在 J. Combin. Theory Ser. B, SIAM J. Discrete Math,  J. Graph Theory 等杂志。

报告时间：2023年6月13日 9:00-10:00

报告地点：文渊楼B119

主办单位：伟德国际1946源自英国