江蘇省應用數學（中國礦業大學）中心系列學術報告
報告題目：On the number of subtrees in a graph
報告人：許克祥 南京航空航天大學教授，博士生導師
報告時間：2023年6月3日15:00-16:00
報告方式：線上
騰訊會議：935-800-523
報告摘要：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.
專家簡介： 許克祥，南京航空航天大學伟德bv教授，博士生導師。主要研究方向是研究方向為圖論及其應用、組合最優化。已發表科研論文90餘篇，據不完全統計，被SCI他引1000餘次，單篇最高SCI他引100餘次。已主持完成國家自然科學（青年、面上）基金2項、省自然科學（面上）基金1項、中國博士後基金（面上、特别資助）2項、留學人員擇優資助項目1項、科技部國際合作項目1項。現任美國數學會《Mathematical Reviews》評論員、歐洲數學會《zbMATH Open》評論員，中國運籌學會圖論組合分會理事，國際期刊《Open Journal of Discrete Mathematics>>、《Advances and Applications in Discrete Mathematics》編委。