报告题目：Enumeration of spanning trees of complete multipartite graphs containing a given spanning forest

报告时间：2022年5月20日上午9：00-10：00

腾讯会议：174 223 218

报告摘要：Moon's classical result implies that the number of spanning trees of a complete graph  with  vertices containing a given spanning forest  equals , where  is the number of components of , and  are the numbers of vertices of component of .  Dong and Ge (Counting spanning trees in a complete bipartite graph which contain a given spanning forest, Journal of Graph Theory, in press) extended this result to the complete bipartite graph, and obtain an interesting formula to count spanning trees of a complete bipartite graph  containing a given spanning forest . They also posed the problem to count spanning trees of a complete -partite graph containing a given spanning forest for . In this paper, we propose a technique to solve this problem. Using this technique, we obtain closed formulae to count spanning trees of complete -partite graphs containing a given spanning forest for  and , which results in a new and simple proof of Dong and Ge's formula. This is joint work with Danyi Li and Wuxian Chen.

个人简介：晏卫根，集美大学教授、博士生导师。2003年7月获厦门大学理学博士学位，2004年10月至2006年12月在台湾“中央”研究院从事博士后研究工作。2010年享受国务院政府特殊津贴。曾获福建省自然科学一等奖、福建省优秀人才与杰出科技人才称号，曾入选福建省百千万人才工程。现为中国组合数学与图论专业委员会委员与福建省运筹学会副理事长。主要研究方向为组合数学与图论及其在统计物理中的应用。在J. Combin. Theory Ser. A，Adv. Appl. Math., Theoret. Comput. Sci.及中国科学A(英文版)等数学期刊上发表学术论文60多篇，已获4项国家自然科学基金面上项目的支持。