# 12月19日 Guangming Jing博士學術報告（數學與統計學院）

Guangming Jing 博士于2019年畢業于Georgia State University, 獲理學博士學位，師從李忠善教授，主要研究方向是圖論及組合。現在是Augusta Univerisity的助理教授。已在J. Graph Theory, J. Combin. Theory Ser. B，Discrete Appl. Math.等國際期刊發表學術論文十余篇，2020年申請到美國國家自然科學基金。

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.

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