主讲人：赖虹建教授，美国西弗吉尼亚大学
报告时间：2020年12月22日9：00
报告地点：腾讯会议 ID：377507287
报告题目：The s-hamiltonian line graph problem
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.
个人简介：赖虹建，美国西弗吉尼亚大学数学系教授，博士生导师。1982年毕业于华南理工大学数学系；1988年获美国维恩州立大学(Wayne State University)理学博士学位，师从组合数学杂志《Journal of Combinatorial Theorey, Series B》的编辑Catlin教授；1988-1989年在加拿大滑铁卢大学(University of Waterloo)组合优化系著名图论专家Bondy教授指导下作博士后研究。赖虹建教授长期从事离散数学的教学和科研工作，主要研究方向为图的哈密顿问题，图论和拟阵论中的欧拉子图问题，染色理论以及相关的整数流和群连通问题。曾主持1996年纪念Catlin教授的欧拉图问题专题会议，第46届和第59届美国中西部图论会议。在《Journal of Combinatorial Theory, Series B》、《Journal of Graph Theory》、《European Journal of Combinatorics》、《Discrete Mathematics》和《Discrete Applied Mathematics》等SCI期刊发表学术论文200余篇，并在Kluwer Academic Publishing出版专著《图与组合学中的矩阵论》，在高等教育出版社出版专著《拟阵论》。
