报 告 人：Guangming Jing 博士
报告题目：Density and Graph Edge Coloring
报告时间：2020年12月19日（周六）上午：9:00-10:00
报告地点：腾讯会议（会议 ID：532577522）
主办单位：数学与统计学院、科学技术研究院
报告人简介：
Guangming Jing 博士于2019年毕业于Georgia State University, 获理学博士学位，师从李忠善教授，主要研究方向是图论及组合。现在是Augusta Univerisity的助理教授。已在J. Graph Theory, J. Combin. Theory Ser. B，Discrete Appl. Math.等国际期刊发表学术论文十余篇，2020年申请到美国国家自然科学基金。
报告摘要：
Given a multigraph $G = (V,E)$, the Chromatic index $\chi'(G)$ is the minimum number of colors needed to color the edges of $G$ such that no two incident edges receive the same color. Let $\Delta(G)$ be the maximum degree of $G$ and let $\Gamma(G) := \max{\frac{2|E(U)|}{|U|-1}: U\subseteq V, |U|\ge 3 \mbox{and odd}}$. $\Gamma(G)$ is called the density of $G$. Clearly, the density is a lower bound for the chromatic index $\chi'(G)$. Moreover, this value can be computed in polynomial time. Quite a few problems and conjectures in this field are related to the density, such as the Overfull conjecture, Seymour's exact conjecture, the Goldberg-Seymour conjecture, and the Core conjecture of Hilton and Zhao. In this talk, we will discuss some recent development on several density-related edge coloring problems.
