报告名称：Removable edges in near-bipartite bricks

报告专家：卢福良

专家所在单位：闽南师范大学

报告时间：2024.3.22

报告地点: 数统学院203

专家简介：卢福良，福建省闽江学者特聘教授。曾入选福建省百千万人才工程。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，省杰青项目等项目多项。在J. Combin. Theory Ser. B, SIAM J. Discrete Math., Journal of Graph Theory等杂志发表论文30余篇。

报告摘要：An edge $e$ of a matching covered graph $G$ is removable if $G-e$ is also matching covered, The notion of removable edge arises in connection with ear decompositions of matching covered graphs introduced by Lov\'asz and Plummer, A nonbipartite matching covered graph $G$ is a brick if it is free of nontrivial tight cuts. Carvalho, Lucchesi, and Murty proved that every brick other than $K 4$ and $\overline(c_6}$ has at least $\Delta-2$ removable edges. A brick $G$ is near-bipartite if it has a pair of edges $\{e_l,e_2\}$such that $G-\(e_1,e_2\}$ is a bipartite matching covered graph. In this paper, we show that in a near-bipartite brick $G$ with at least six vertices, every vertex of $G$, except at most six vertices of degree three contained in two disjoint triangles, is incident with at most two nonremovable edges; consequently, $G$ has at least $\frac{|V(G)|-6}{2}$ removable edges. Moreover, all graphs attaining this lower bound are characterized.