报告人：陆由教授

报告时间：2025年11月25日9:00

腾讯会议：426-405-918

报告摘要：Jaeger, Linial, Payan and Tarsi (JCTB, 1992) introduced the concept of group connectivity as a generalization of Tutte's integer flow for ordinary graphs and  proposed a conjecture that every $5$-edge-connected graph is $Z_3$-connected.  Lov\'asz, Thomassen, Wu and Zhang (JCTB, 2013) proved that every $6$-edge-connected graph is $Z_3$-connected.

Li, Luo, Ma and Zhang (DM, 2018) extended group connectivity of ordinary graphs to $2$-unbalanced signed graphs and conjectured that every $5$-edge-connected $2$-unbalanced signed graph is $Z_3$-connected. This conjecture was verified only for $11$-edge-connected signed graphs, for $6$-edge-connected signed graphs with negativeness $2$ or $3$, for $5$-edge-connected signed $K_4$-minor-free graphs, and for signed complete graphs on at least $6$ vertices.

In this paper, we prove that this conjecture holds for $5$-edge-connected signed graph with independence number at most two. The $5$-edge-connectivity cannot be reduced to $4$-edge-connectivity. This work is joint with Xiao Wang and Zhengke Miao.

报告人简介：陆由，西北工业大学教授，博士生导师。现担任中国工业与应用数学学会图论组合及应用专委会常务委员、陕西省工业与应用数学学会常务理事。从事图论及其应用研究，先后承担国家自然科学基金项目3项，承担省自然科学基金项目2项，参与国家自然科学基金重点项目1项；在J Combin Theory Ser B、J Graph Theory、SIAM J Discrete Math、European J Combin等期刊上发表学术论文40余篇；获陕西高等学校科学技术研究优秀成果一等奖1项，陕西省自然科学优秀学术论文二等奖1项、陕西省工业与应用数学学会青年优秀论文一等奖1项。

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