报告名称: 2-walks in 3-connected cubic planar graphs

报告专家：崔庆

专家所在单位：南京航空航天大学

报告时间：2024年3月22日

报告地点: 数统学院409

专家简介：崔庆，南开大学博士，美国佐治亚州立大学访问学者，现为南京航空航天大学数学学院教授、硕士生导师。主要研究方向包括图的圈结构、图的分解问题等，主持国家自然科学基金项目2项，在J.Combin.Theory Ser.B、J.Graph Theory、SIAM J. Discrete Math等期刊发表论文 30 余篇。

报告摘要：A $k$-walk in a graph $G$ is a spanning closed walk passing through each vertex at most $k$ times, In 1994, Gao and Richter proved that every 3-connected planar graph has a 2-walk, confirming a conjecture of Jackson and Wormald, In 2009, Nakamoto, Oda and Ota further asked for an upper bound on the  number of vertices visited twice of 2-walks in 3-connected planar graphs. We consider a special case of this problem, and show that every 3-connected cubic planar graph with $n$ vertices has a 2-walk in which the number of vertices visited twice is at most $\frac {n-1}{3}$.