应太阳成tyc7111cc邀请，兰州大学张和平教授将与太阳成t官网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，兰州大学太阳成tyc7111cc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
太阳成tyc7111cc
