报告人：张和平（兰州大学 教授）
报告时间：2024年11月 10日(周日)下午15:00
报告地点：章辉楼442
联系人：晏卫根教授
欢迎广大师生参加！
报告摘要： As a common generalization of factor-critical and bicritical graphs O. Favaron and Q. Yu independently 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 if the 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 described 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 for S. Norine and R. Thomas' conjecture on the number of cubic vertices of minimal bricks. This is a joint work with Dr. Jing Guo.
报告人简介：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委员（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、化学图论等方向的研究，发表了200余篇SCI 收录学术论文，主持了国家自然科学基金项目8项，包括重点项目“应用图论”。曾在香港浸会大学，法国巴黎南大学，澳大利亚Newcastle大学，美国中田纳西州立大学，台湾中研院数学所学术访问。
