江苏省应用数学（中国矿业大学）中心系列学术报告
报告题目：On the number of subtrees in a graph
报告人：许克祥 南京航空航天大学教授，博士生导师
报告时间：2023年6月3日15:00-16:00
报告方式：线上
腾讯会议：935-800-523
报告摘要：The study on the number of subtrees 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 above topics 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 the connected graphs of order $n$ with $k$ cut edges, cacti of order $n$ with $k$ cycles, and block graphs of order $n$ with $k$ blocks, respectively. And a partial solution is provided to a conjecture for the mean subtree order of trees posed in 1984. Moreover, the extremal tree is determined with the second smallest mean subtree order. Furthermore, a complete solution is obtained to a conjecture of the probability that a random subtree of $K_n$ contains a given edge.
专家简介： 许克祥，南京航空航天大学数学学院教授，博士生导师。主要研究方向是研究方向为图论及其应用、组合最优化。已发表科研论文90余篇，据不完全统计，被SCI他引1000余次，单篇最高SCI他引100余次。已主持完成国家自然科学（青年、面上）基金2项、省自然科学（面上）基金1项、中国博士后基金（面上、特别资助）2项、留学人员择优资助项目1项、科技部国际合作项目1项。现任美国数学会《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 Journal of Discrete Mathematics>>、《Advances and Applications in Discrete Mathematics》编委。