时间：2023年6月14日     星期三  9:00-11:00

地点：东校区二教203

报告题目：The s-hamiltonian line graph problem

报告人：赖虹建教授            

邀请人：游志福

报告摘要：Thomassen posed the conjecture that every 4-connected line graph is hamiltonian in 1984. Matthews-Sumner conjectured that every 4-connected claw-free graph is hamiltonian. In 1999, Ryjachek introduced the line graph closure of a claw-free graph and showed that the two conjectures above are equivalent. In 2004, Kuczel and L. Xiong further conjectured that every 4-connected line graph is hamiltonian-connected, and in 2011, Ryjachek and Vrana conjectured that every 4-connected claw-free graph is hamiltonian connected, and showed that all 4 conjectures presented above are equivalent. All these conjectures are sufficient conditions. In 1987, Broersma and Veldman raised the problem to investigate necessary and sufficient conditions for a line graph to be s-hamiltonian. In this talk, we will present our considerations of seeking necessary and sufficient condition version of the Thomassen conjecture in the format of the s-hamiltonian line graphs and claw-free graphs, and the related developments and progresses.

报告人简介：美国西弗吉尼亚大学数学系终身教授，博士生导师，国际知名的图论专家，主要研究领域包括图论中的欧拉子图、哈密尔顿性问题、整数流以及图论中的染色和连通度问题，出版学术著作两部，发表学术论文250余篇。完成了两部专著：由克鲁亚学术出版社（Kluwer Academic Publishing）出版的“图与组合学中的矩阵论”和由高等教育出版社出版的“拟阵论”。1996年获学院最优科研奖，2006年获学院最优教师奖和全校最优教师奖，成为西弗吉尼亚大学历史上第一个获此荣誉的华裔教授。曾主持过1996年由美国国家自然科学基金会资助的纪念凯特林（Catlin）教授的欧拉图问题专题会议，2008年由美国国家自然科学基金会资助的第46届美国中西部图论会议，以及2018年的第59届美国中西部图论会议。曾任Discrete Mathematics杂志客座编辑，现担任Applied Mathematics和Graphs and Combinatorics等多个杂志的编辑。

  欢迎各位老师同学们前来参加！

数学与系统科学学院