报告题目：Cosupereulerian graphs
报 告 人：赖虹建，西弗吉尼亚大学
报告时间：2025年5月6日（周二）上午11：00-12：00
报告地点：广东工业大学龙洞校区行政楼610
主 持 人：何伟骅
报告摘要： A subset $S$ of a matroid $M$ is eulerian if $S$ is a disjoint union of circuits. A matroid with an eulerian subset spanning in $M$ is supereulerian, and a connected graph $G$ is supereulerian if its cycle matroid $M(G)$ is supereulerian. A graph $G$ is cosupereulerian if its cocycle matroid $M^*(G)$ is supereulerian. In [J. of Graph Theory, 664 (2010), 1-11], it is proved that every 3-edge-connected graph with circumference at most 8 is supereulerian. This result can be improved to the form that every 3-edge-connected graph $G$ with circumference at most 9 is supereulerian if and only if $G$ does not have a block isomorphic to the Petersen graph. We introduce cosupereulerian reductions of graphs in the sense that a graph $G$ is cosupereulerian if and only if its cosupereulerian reduction is cosupereulerian; and determine a finite family $F$ of non cosupereulerian graphs such that any simple graph $G$ with every bond size at most 9 is cosupereulerian if and only if its cosupereulerian reduction has a block lying in $F$.
专家简介：赖虹建，美国西弗吉尼亚大学教授、博士生导师，1988获美国密执安韦恩州立大学（Wayne State University）数学博士学位，1988-1989年在加拿大滑铁卢大学（University of Waterloo）组合优化系从事博士后研究。从2009年起任西弗吉尼亚大学数学系副主任、系主任。1996年获学院最优科研奖， 2006年获学院最优教师奖，以及2006年全校最优教师奖， 成为西弗吉尼亚大学历史上获此荣誉的第一个华裔教授。
