报告名称:On extremal nonsolid bricks
主办单位:永利集团88304官网
报告专家:卢福良
专家所在单位:闽南师范大学
报告时间:2021年1月8日14:00
报告地点:腾讯会议(会议ID:238 525 244)
专家简介:卢福良,“闽江学者”特聘教授,闽南师范大学首批“龙江学者”特聘教授,先后主持国家自然科学基金项目3项。主要研究兴趣:图的匹配理论、边染色等,已在Electron. J. Comb.、SIAM J. Discrete Math.、J. Graph Theory等期刊发表论文20余篇。
报告摘要:A3-connected graph is a brick if, after the removal of any two distinct vertices, the resulting graph has a perfect matching. Lovasz [Matching structure and the matching lattice, J. Combin. Theory (B) 43 (1987), 187-222] proved that the dimension dim(G) of the matching lattice of a brick G is equal to |E(G)|−|V (G)| + 1. We say a brick G is extremal if the number of perfect matchings in G is exactly dim(G).
De Carvalho, Lucchesi and Murty [Graphs with independent perfect matchings, Jour- nal of Graph Theory 48 (2005), 19-50] characterized extremal bricks and conjectured that every extremal nonsolid brick other than the Petersen graph is the result of the splicing of an extremal brick and a K4, up to multiple edges. In this talk, we present an infinite family of graphs showing that this conjecture fails. This is a joint work with Xing Feng.
邀请人:刘慧清