报告题目：Cosupereulerian graphs

报告人：赖虹建教授

报告时间：2025年5月14日 16:00-17:00

报告地点：科技园阳光楼南815

邀请单位：数学与统计学院、离散数学及其应用省部共建教育部重点实验室

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 the 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 either cosupereulerian, or its cosupereulerian reduction has a block in $F$.

报告人简介：赖虹建教授是美国西弗吉尼亚大学数学系终身教授，博士生导师，国际知名的图论专家，主要研究领域包括图论中的欧拉子图、哈密尔顿性问题、整数流以及图论中的染色和连通度问题，出版学术著作两部，在JCT(B),Combinatorica，SIAM J.DM.,JGT,Europ.J.Combin., EJC, DM等杂志发表学术论文250余篇。完成专著2部，分别是《图与组合学中的矩阵论”(Kluwer Academic Publishing)》、《和的“拟阵论”》(高等教育出版社)。曾任DM杂志客座编辑，现担任Applied Mathematics和Graphs and Combinatorics等多个杂志编委。

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