应pc加拿大预测准确率张和平教授和高毓平副教授邀请，美国奥本大学镡松龄助理教授将于2023年12月12日-12月24日访问兰州大学，期间于12月14日举办学术报告。

报告题目：Graph Edge Coloring and the Overfull Conjecture

报告时间：2023年12月14日下午4:00

报告地点：城关校区理工楼631

报告摘要：Let $G$ be a simple graph. An edge coloring of $G$ is an assignment of colors to the edges of $G$ so that any two adjacent edges receive distinct colors. The smallest number of colors needed in such an assignment is the chromatic index of $G$. Clearly, we need at least $\Delta(G)$, the maximum degree of $G$, this many colors. On the other hand, Vizing in 1965 proved that at most $\Delta(G)+1$ colors are sufficient. According to their chromatic index, we naturally classify all simple graphs into class 1 (those with chromatic index equal to their maximum degree) or class 2, but the classification problem is NP-complete. However, when a graph has ``too many’’edges, the graph is trivially class 2. Conversely, Chetwynd and Hilton in 1985 made the Overfull Conjecture: if a graph $G$ satisfies $\Delta(G)>|V(G)|/3$, then $G$ is class 2 also implies that $G$ or some subgraph of $G$ has too many edges. In this talk, we look at some recent progress toward the conjecture.

欢迎广大师生参加！

报告人简介

镡松龄，美国奥本大学助理教授，主要研究方向为结构图论、图染色与极值图论。于2015年从美国佐治亚州立大学获得博士学位，2015-2018年在美国范德堡大学从事博士后研究工作。截止目前，在J. Combinatorial Theory Ser. B，J. Graph Theory等图论与组合方向的顶级期刊发表高水平学术论文四十几篇，解决了图论领域的几个公开问题和猜想。

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2023年12月11日