报告学者：Hong-Jian Lai

报告者单位：西弗吉尼亚大学

报告时间：2025年11月17日下午4：00---5：00

报告地点：SY202

报告摘要： Motivated by Thomassen’s conjecture that every 4-connected line graph is Hamiltonian, and as line graphs are $K_{1,3}$-free graphs, many researchers have investigated the Hamiltonian properties of graphs forbidding certain induced graphs including $K_{1,3}$. The hourglass $\Gamma_0$ is the unique simple graph with degree sequence $(4,2,2,2,2)$ and $P_n$ is the path on $n$. In [Discrete Mathematics 341 (2018) 1806-1815],  Z. Ryj\'{a}\v{c}ek, P. Vr\'{a}na and L. Xiong posed a conjecture that every 3-connected $\{K_{1,3}, \Gamma_0, P_{16}\}$-free  graph is Hamilton-connected. X. Liu and L. Xiong proved this conjecture in [Discrete Mathematics 345(2022), 112910] proved this conjecture. We continue to study this problem aiming to characterize all extremal graphs. We have found a family ${\cal W}$ of graphs formed by subdividing the Wagner graph and by attaching pendent vertices, and prove that every 3-connected $\{K_{1,3}, \Gamma_0, P_{18}\}$-free graph $G$ is Hamilton-connected unless the Hamilton-connected closure of $G$ is a member of ${\cal W}$.

报告者简介：赖虹建教授是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，在JCT(B),Combinatorica，SIAM J.DM.,JGT,Europ.J.Combin., EJC, DM等杂志发表学术论文250余篇，完成专著2部。曾任DM杂志客座编辑，现担任Applied Mathematics和Graphs and Combinatorics等多个杂志编委。