报告题目：On the number of subgraphs in a graph

报 告 人：许克祥 教授

报告时间：2025 年 6 月16 日 （周一）19:30-20:30

报告地点：腾讯会议（465-102-039）

报告摘要：The study on the number of subgraphs in a graph is a hot topic in enumerative combinatorics with some related problems. Extremal problems in this field are much attractive in graph theory. Many results are published on the number of subtrees for trees, but there are few results for the general graphs. In this talk we characterize the extremal graphs with the number of subtrees among all connected graphs of order n with s cut edges, cacti of order n with s cycles, and block graphs of order n with s blocks, respectively. And a partial solution is provided to a conjecture for the mean subtree order of trees posed in 1984. Moreover, several results are proved for the local and global mean orders of sub-k-trees of k-trees. Furthermore, a complete solution is obtained to a conjecture of the probability that a random subtree of Kn contains a given edge.

报告人简介：许克祥，男，南京航空航天大学数学学院教授，博士生导师，研究兴趣：图论及其应用。主持完成国家自然科学基金及省部级科研基金6项，获江苏省高等教育成果（高校自然科学类）三等奖1项（排名1/3）。迄今发表学术论文100余篇，其中SCI 收录90余 篇，他引用近千余次，出版英文专著和中文教材各1部。