一、题目

Chvátal-Erdős Conditions and Almost Spanning Trails

二、主讲人

Hongjian Lai

三、摘要

The well-knownChvátal-Erdős Theorem on hamiltonian graphs states that if the stability number a(G) and the connectivity k(G) satisfy the conditionk(G)>a(G)+s,where s{-1,0,1} then G has a Hamilton path if s=-1, a Hamilton cycle ifs=0and G is Hamilton-connected ifs=1.There have been many efforts to generalize theChvátal-Erdős Conditions and similar conditions in graph theory. We will present some of these extensions. In particular, we will share the ideas of our effort to extend theChvátal-Erdős Theorems within the family of all line graphs.

四、主讲人简介

赖虹建，美国西弗吉尼亚大学终身教授、博导。主要研究工作包括：图论和拟阵论中的欧拉子图问题、哈密顿圈以及哈密顿性问题、整数流问题、等密拟阵和等密网络问题、图论中的染色问题和连通度问题,Journal of Combinatorial Theory(Series B)、Applied Mathematics and Computation、Journal of Graph Theory、Discrete Applied Mathematics等核心杂志上发表学术论文250余篇。现任《Applied Mathematics》和《Graphs and Combinatorics》等杂志编辑。

五、邀请人

颜谨 数学学院教授

六、时间

1月7日（周四）9:00-10:00

七、地点

腾讯会议号：730 753 656

八、主办方

山东大学数学学院