报告时间: 6月10日下午 15:00—17:00

报告地点：腾讯会议，会议号：389794741

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)

报告摘要: The study on the number of subtrees in a graph is a hot topic in enumerative combina- torics 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 num- ber 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 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，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、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90余篇，其中SCI 收录70余 篇，他引用近千余次，出版英文专著和中文教材各1部。

报告题目：On even cycle decompositions of 4-regular graphs

报告人: 崔庆(南京航空航天大学副教授)

报告摘要：An even cycle decomposition of a graph is a partition of its edges into even cycles. It is well-known that a connected graph admits a cycle decomposition if and only if it is Eulerian. However, there is no known necessary and sufficient condition for a graph to have an even cycle decomposition. In 2012, Markstrom conjectured that the line graphs of 2-connected cubic graphs have even cycle decompositions. In this talk, we will introduce the recent progress on Markstrom’s conjecture and related problems.

报告人简介：崔庆，南开大学博士，美国佐治亚州立大学访问学者，现为南京航空航天大学数学学院副教授、硕士生导师。主要研究方向包括图的圈结构、图的分解问题等，主持国家自然科学基金项目2项，在J. Combin. Theory Ser. B、J. Graph Theory、SIAM J. Discrete Math.、European J. Combin.等期刊发表论文20余篇。