It is conjectured by Berge and Fulkerson thatevery bridgeless cubic graph has six perfect matchings such that each edge iscontained in exactly two of them. Berge-Fulkerson conjecture holds for 3-edgecolorable cubic graphs. A snark is a cyclically $4$-edge connected cubic graphof girth at least 5 admitting no $3$-edge coloring. In this talk, we will gavesome progress regarding this conjecture for some snarks and related issues.

郝荣霞，北京交通大学教授, 博士生导师。主要从事图论和网络的研究，在IEEE TC、IEEE TPDS、European J. Combin.、J. Graph Theory，SIAM J. Discrete Math.等国内外学术期刊上发表论文100余篇。主持和参加国家自然科学基金面上项目多项。参加国家自然基金重点和国际合作与交流项目三项。第八届国际华人数学家大会做45分钟邀请报告。曾获北京市高等教育教学成果一等奖、北京运筹学会青年优秀论文一等奖，北京交通大学“巾帼十杰”、“毕业生我最敬爱的教师”、“教学名师”和“智瑾奖教金优秀教师奖”等奖项。国际期刊International Journal of Computer Mathematics: ComputerSystems Theory的编委。