报告题目：The Goldberg-Seymour Conjecture

报告人：Guantao Chen(陈冠涛)，教授，Georgia State University(美国佐治亚州立大学)

照片：

邀请人：邹青松

报告时间：2019年5月4日08: 50

报告地点：北校区阶梯教室J-112

报告人简介：

陈冠涛教授,美国佐治亚州立大学杰出教授(Distinguished University Professor)、数学与统计系系主任，华中师范大学湖北省人才计划特聘教授，国际图论界权威期刊《图与组合》(Graphs and Combinatorics)执行编委。陈冠涛教授主要从事图论领域中的结构图论、极图理论、Ramsey理论等方向的基础理论研究，多次主持美国国家自然科学基金面上项目，在Journal of Combinatorial Theory Series B, Journal of Graph Theory, SIAM J. Discrete Mathematics和SIAM J. Computing等权威学术期刊上发表论文100余篇, 证明了十余个重要猜想，受到同行广泛的尊敬,并在2001年被美国佐治亚州立大学授予杰出成就奖（The Outstanding Achievement Faculty Award）。

报告摘要：

Given a multigraph , the edge-coloring problem (ECP) is to color the edges of G with the minimum number of colors so that no two adjacent edges have the same color. This problem can be naturally formulated as an integer program, and its linear programming relaxation is called the fractional edge-coloring problem (FECP). In the literature, the optimal value of ECP (resp. FECP) is called the chromatic index (resp. fractional chromatic index) of G, denoted by (resp. ). Let be the maximum degree of G and let . Clearly, is a lower bound for . As shown by Seymour, . In the 1970s Goldberg and Seymour independently conjectured that . Over the past four decades this conjecture, a cornerstone in modern edge-coloring, has been a subject of extensive research, and has stimulated a significant body of work. I will report the proof of this conjecture and problems surrounding this conjecture.

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