报告题目1：On removable edges in matching covered graphs
报告人：王秀梅教授，郑州大学
报告时间：2024年11月4日（周一）15:00-16:00
会议地点：腾讯会议：139-252-475
摘要：A graph G is matching covered if each edge of G is contained in a perfect matching of G. An edge e of a matching covered graph G is removable if G – e is also matching covered. This talk presents some results on removable edges in matching covered graphs, including the characterizations of graphs without removable edges and the number of removable edges in a graph.
报告人简介：王秀梅，郑州大学数学与统计学院教授、博导，中国运筹学会常务理事，中国运筹学会图论组合分会常务理事，中国运筹学会数学规划分会理事，河南省运筹学会常务理事。主要从事图论与组合最优化的研究工作，研究工作主要集中在图的匹配理论，包括圈结构和完美匹配，及匹配覆盖图的可去边的研究。代表性工作是用最少的匹配覆盖图的顶点集这一问题给出了多项式时间算法；对于完美匹配多面体的1-骨架图是完全图的图，在二部图、几乎二部图等若干图类给出了完整的刻画。
报告题目2：Planar wheel-like bricks
报告人：卢福良教授，闽南师范大学
报告时间：2024年11月4日（周一）16:00-17:00
会议地点：腾讯会议：139-252-475
摘要：An edge $e$ in a matching covered graph $G$ is removable if $G-e$ is matching covered; a pair $\{e,f\}$ of edges of $G$ is a removable doubleton if $G-e-f$ is matching covered, but neither $G-e$ nor $G-f$ is. Removable edges and removable doubletons are called {\em removable classes}, which was introduced by Lovasz and Plummer in connection with ear decompositions of matching covered graphs.
A brick is a nonbipartite matching covered graph without nontrivial tight cuts. A brick $G$ is wheel-like if $G$ has a vertex $h$, such that every removable class of $G$ has an edge incident with $h$. Lucchesi and Murty conjectured that every planar wheel-like brick is an odd wheel. We present a proof of this conjecture.
报告人简介：卢福良，闽南师范大学，福建省闽江学者特聘教授。主要研究兴趣是图的匹配理论及相关问题，主持国家自然科学基金委面上项目等多项项目。在J. Combin. Theory Ser. B,SIAM J. Discrete Math., Journal of Graph Theory，Electron. J. Comb.，Discrete Math.等杂志发表论文40余篇。