报告题目:On the number of subgraphs in a graph
报 告 人:许克祥,南京航空航天大学,教授
报告摘要:The study on the number of subgraphs in a graph is a hot topic in enumerative combi-natorics with some related problems. Extremal problems in this ?eld 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. Fur-thermore, 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,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。已主持完成国家自然科学基金多项、省部级科研项目(包括江苏省自然科学基金、科技部国际合作项目等)多项。发表科研论文100余篇,被SCI他引1000余次,单篇最高SCI他引100余次,出版英文专著和中文教材各1部。2018年获江苏省高等教育成果(高校自然科学类)三等奖1项,2023年入选全球前2%顶尖科学家榜单。
报告时间:2024年6月22日10:10-10:50
报告地点:文渊楼B208
主办单位:数学与统计学院