报告名称：On extremal nonsolid bricks

主办单位：英国立博官网中文版

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