您的位置: 首页 > 资源和办公 > 新闻中心 > 学术报告

罗荣教授学术讲座预告

讲座题目:  Some results on group connectivity

讲座时间:  2017.7.28 9:00---10:30

讲座地点:  9号楼6层会议室

主讲人:  罗荣教授

内容摘要:  
The concept of  group connectivity was introduced by Jaeger, Linial, Payan, and Tarsi (Journal Combinatorial Theory, Ser. B, 1992)  as a generalization of nowhere-zero group flows. Let A be an Abelian group.  An A-connected graphs are contractible configurations of A-flow and play an important role in the  study of group flows because of the fact: if H is A-connected, then any supergraph G of H (i.e. G contains H as a subgraph) admits a nowhere-zero A-flow if and only if G/H does.   It is known that an A-connected graph cannot be very sparse.  How dense could an A-connected graph be?   This motivates us to study the extremal problem: find the maximum integer k, denoted ex(n, A), such that every graph with at most k edges is not A-connected. We determine the exact values for all finite cyclic groups.  As a corollary, we present a characterization of all Z_k-connected graphic sequences.  As noted by Jaeger, Linial, Payan, and Tarsi,  there are Z_5-connected graph that are not Z_6-connected. We  also prove that every Z_3-connected graph contains two edge-disjoint spanning trees, which implies that every Z_3-connected graph is also A-connected for any Abelian group A with order at least 4.
主讲简介:  
罗荣,美国西弗吉尼亚大学(West Virginia University,USA)数学系教授。主要研究图的染色理论和流的理论,是国际知名的染色问题专家。发表50余篇论文,多数是发表在图论顶尖杂志上,如Journal of Cominatorial Theory Ser. B,  Journal of Graph Theory,  SIAM Journal on Discrete Math,  European J. of Combinatorics.  在上世纪60年代末Vizing提出的四个关于边染色猜想的研究方面取得了一系列突破性进展。解决了几个著名的公开问题,如Erdos、Gould Jacobson以及 Lehel 提出的一个关于可图序列猜想,Borodin 提出的边面染色的问题,以及Archdeacon 关于三流可图序列的问题。

快速通道

FAST TRACK