报告题目：PROBLEMS AND RECENT RESULTS SURROUNDING THE GOLDBERG-SEYMOUR CONJECTURE

报告人：陈冠涛教授

报告时间：2025年5月14日 15:00-16:00

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：The Goldberg-Seymour Conjecture, now confirmed, states that for any (multi)graph $G$, if the chromatic index $\chi'(G) > \Delta(G) + 1$, then $\chi'(G) = \Gamma(G)$, where $\Delta(G)$ denotes the maximum degree of $G$ and $\Gamma(G)$ is the \emph{density} of $G$, defined as the ceiling of $2|E(H)|/(|V(H)|-1)$ taken over all subgraphs $H \subseteq G$ with $|V(H)|$ odd. In terms of edge-coloring critical graphs, the conjecture asserts that if $G$ is a critical graph with $\chi'(G) > \Delta(G) + 1$, then for every edge $e \in E(G)$, the graph $G-e$ is a union of disjoint near-perfect matchings. The resolution of this conjecture yields a classification of loopless multigraphs with respect to their chromatic index and has potential implications for several other well-known problems in graph coloring, including the Total Coloring Conjecture, the Berge-Fulkerson Conjecture, and the List Coloring Conjecture. In this talk, we will outline these connections and discuss some related open problems.

报告人简介：陈冠涛，佐治亚州立大学教授，数学与统计系主任。主要研究方向为图论及其应用。主要研究图的结构问题，如图的圈和路、图染色和图的Ramsey理论。近年来，他的主要工作是研究对图的边进行重新着色的技巧，并利用它们解决该领域的一些经典问题。他在组合学和图论的主要期刊上发表了120多篇论文，并与他的许多合作者解决了许多长期存在的猜想。曾担任SIAM离散数学活动组的组织者(2014-2016)，以及《图与组合学》杂志的执行主编(2011年以来)。

欢迎老师和同学们参加！