报告时间：2025年11月19日（周三）上午9:00

报告地点：Meeting number (access code): 2533 337 8417；Meeting password: Aw69JAHWQq8

报告人简介: 陈冠涛，美国佐治亚州立大学教授、Graphs and Combinatorics 主编（Editor-in-Chief)

报告摘要：A connected graph G is called a matching covered graph if E(G)= and every edge E(G) is contained in a perfect matching, a matching that covers every vertex of G. A matching covered graph G is bicritical if, for any two distinct vertices xy V (G), the graph G x y has a perfect matching. A 3-connected bicritical graph is called a brick, and it is minimal if the removal of any edge from G results in a graph that is no longer a brick. Lovasz conjectured that every minimal brick contains two adjacent cubic vertices. In this talk, we show that every minimal brick contains two cubic vertices whose distance is at most 2. Additionally, we verify Lovaszs conjecture for minimal bricks with an average degree of at least 45. As a corollary, we deduce that every minimal brick contains two adjacent vertices of degree at most 5.