主讲人：陈冠涛教授，美国佐治亚州立大学

报告时间：2020年8月28日10：00

报告地点：腾讯会议 ID：947 805 118

报告题目：Critical Edge Chromatic Graphs

**报告摘要：**Vizing’s classic result states the chromatic index $\chi'(G) = \Delta(G) $ or $\Delta(G) +1$ where $\Delta(G)$ is the maximum degree of G. Consequently, simple graphs are divided into families: class one and class 2. By a result of Holyer, determining chromatic index is an NP-hard problem. In investigating the classification problem, critical graphs are of particular interest. A graph G is called critical if $\chi'(H)<\chi'(G)$ for every proper subgraph H of G. Critical graphs of class two have rather more structure than arbitrary graphs of class two, and it follows from Vizing’s theorem that every graph of class two contains a critical graph of class two with the same maximum degree as a subgraph. These facts can be used when proving results in relation to the classification problem. By developing some new recoloring techniques beyond Vizing fan, we have made some progress on a number of long-standing problems regarding edge a critical class two graphs, such as Vizing’s average degree conjecture and Hilton-Zhao’s core conjecture. We will give a summary of our recently results. Applications to a number of classic problems in critical class 2 simple graphs.

**个人简介：**Guantao Chen, is the Regent’s Professor and the Chair of the Department of Mathematics and Statistics, Georgia State University. His research interests are mainly in graph theory and its applications. He works on graph structural problems in several areas, such as cycles and paths in graphs, graph coloring, and graph Ramsey theory. In recent years, most of his efforts have been in developing and understanding graph edge recoloring techniques and using them to solve some classic problems in the area. He has published more than 120 papers in major journals in combinatorics and graph theory and, with various of his collaborators, solved a number of long standing conjectures. He served as the Program Coordinator of the SIAM Discrete Mathematics Active Group (2014-2016) and a Managing Editor of the journal of Graphs and Combinatorics since 2011.

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