应数学与统计学院邀请，兰州大学张和平教授将与我院师生在线下做学术交流并做专题学术报告。
报告题目：Minimum degree of minimal k-factor-critical graphs
报告摘要：As a common generalization of factor-critical and bicritical graphs O. Favaron and Q. Yuindependently introduced $k$-factor-critical graphs.A graph $G$ of order $n$ is said to be $k$-factor-critical for an integer $1\leq k< n$,if the removal of any $k$ vertices results in a graph with a perfect matching.A $k$-factor-critical graph is minimal ifthe deletion of every edge results in a graph that is not $k$-factor-critical.In 1998, O. Favaron and M. Shi proposed a question: Is it true that every minimal $k$-factor-critical graph has minimum degree $k+1$? and gave a positive answer for for $k=1, n-2, n-4$ and $n-6$. Afterwards in 2007 Z. Zhang et al. formally describe it as a conjecture, which remains open to now in general case. This talk will present some recent progresses on this topic: J. Guo and H. Zhang have confirmed this conjecture for $k=2, n-8, n-10$ by using a new method. As joint works with Dr. F. Lu and Q. Li, very recently this conjecture has also be confirmed for claw-free graphs and planar graphs. Moreover, we derive that every 3-connected minimal bicritical claw-free graph $G$has at least $\frac{1}{4}|V(G)|$ cubic vertices, yielding further evidence forS. Norine and R. Thomas' conjecture on the number of cubic vertices of minimal bricks.
This is a joint work with Dr. Jing Guo.
报告时间：2024年12月20日15:00
报告地点：致勤楼（原教学9号楼）D08
邀 请 人：陈祥恩教授、刘霞副教授、姚海元副教授
届时欢迎广大师生参与交流！
报告人简介：
张和平，兰州大学数学与统计学院教授（二级）、博士生导师。1994年获四川大学博士学位，1999年晋升教授，2001年任博士生导师，2001年获教育部“第三届高校青年教师奖”，2002年获国务院颁发的政府特殊津贴，2009年入选甘肃省领军人才（2层次），2014年6月当选国际数学化学科学院院士（Member of the International Academy of Mathematical Chemistry）。现任中国组合数学与图论学会常务理事。主要从事图的匹配理论、化学图论及网络等方向的研究，发表SCI 收录学术论文200余篇，主持国家自然科学基金项目8项，包括重点项目“应用图论”。曾赴香港浸会大学，法国巴黎南大学，澳大利亚Newcastle大学，美国中田纳西州立大学，台湾中研院数学所进行学术访问。
甘肃省数学与统计学基础学科研究中心
数学与统计学院
