报告名称:Removable edges in near-bipartite bricks
报告专家:卢福良
欧洲杯赛事专家所在单位: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。主要研究欧洲杯决赛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.欧洲杯赛事, 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 removabl欧洲杯冠亚军e if $G-e$ is also matching covered, The notion of removable edge arises in connection wit欧洲杯赛事h ear decompositions of matching covered graphs introduced by Lov\'asz and Plummer, A nonb欧洲杯冠亚军ipartite matching covered graph $G$ is a brick if it is free of nontrivial tight cuts. Car欧洲杯投注valho, 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-欧洲杯预测bipartite if it has a pair of edges $\{e_l,e_2\}$such that $G-\(e_1,e_2\}$ is a bipartite 欧洲杯预测matching covered graph. In this paper, we show that in a near-bipartite brick $G$ with at 欧洲杯投注least six vertices, every vertex of $G$, except at most six vertices of degree three conta欧洲杯赛事ined in two disjoint triangles, is incident with at most two nonremovable edges; consequen欧洲杯投注tly, $G$ has at least $\frac{|V(G)|-6}{2}$ removable edges. Moreover, all graphs attaining 欧洲杯决赛this lower bound are characterized.