讲座题目：On the number of subgraphs in a graph

讲座时间：2023.11.12（周日）10：00-11：00

讲座地点：腾讯会议126-997-828

主讲人：许克祥

主讲内容：

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.

主讲人简介：

许克祥，男，南京航空航天大学数学学院教授，博士生导师，美国数学会《Mathematical Reviews》评论员，欧洲数学会《zbMATH Open》评论员，中国运筹学会图论组合分会理事，国际期刊《Open Joutnal of Discrete Mathematics>>、《Advances and Applications in Discrete Mathematics》编委。研究兴趣：图论及其应用，包括极值图论、度量图论、化学图论及计数组合等。主持完成国家自然科学基金、江苏省自然科学基金、国家科技部国际合作项目及中国博士后基金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（接受）发表学术论文100余篇，其中SCI 收录80余 篇，他引用近千余次，出版英文专著和中文教材各1部。