一、题目：

Path Extendable Tournaments

二、主讲人：

张赞波

三、摘要：

A digraph is called path extendable if for every nonhamiltonian (directed) path in , there exists another path with the same initial vertex and terminal vertex of , and for a vertex Hence, path extendability implies path of continuous lengths between every vertex pair. In earlier works of C. Thomassen and K. Zhang, it has been shown that the condition of small or positive implies paths of continuous lengths between every vertex pair in a tournament , where is the irregularity of and stands for the minimum number of paths of length 2 from to among all vertex pair . Motivated by these results, we studied sufficient conditions in terms of and that guarantee a tournament is path extendable. We prove that a tournament is path extendable if . As a corollary we get that a tournament is path extendable if . As a direct application of the last result, we use it to deduce that almost all random tournaments are path extendable.

四、主讲人简介：

张赞波，现为广东财经大学统计与数学学院教授，先后在中山大学和荷兰特文特大学（University of Twente）获得计算机和应用数学方向博士学位，曾为广东省"千百十"人才培养工程省级培养对象。主要从事图论及其算法等方面研究工作，在SIAM J. on Discrete Mathematics, J. of Graph Theory等国际学术期刊上发表论文约三十篇，完成学术著作两部，在图的匹配理论，路圈理论，图划分算法和连通度算法等方向上取得系列成果，部分基础性成果被相关领域的专著和综述所引用。主持完成广东省自然科学基金项目两项，广东省重点科研项目一项，现主持广东省自然科学基金项目一项。

五、邀请人：

颜谨 数学学院教授

六、时间：

5月10日（周二）15:00-16:00

七、地点：

腾讯会议

联系人：颜谨，联系方式：139 6405 5656

八、主办：

山东大学数学学院