报告题目：Group Connectivity, Spanning Trees, Realization of A-connected Sequences

报告人：罗荣教授西弗吉尼亚大学

邀请人：朱强副教授

报告时间：2016年6月6日下午2：40

报告地点：信远楼II206数统院报告厅

报告人简介：

罗荣，美国西弗吉尼亚大学（WestVirginia University，USA）数学系教授、博士生导师，美国数学学会委员，曾任中西部图论会议、AMS东南会议图论会议、坎伯兰会议大会组委会委员，现任Journal of Proteomics & Bioinformatics，Open Journal of Discrete Mathematics，ISRN Discrete Mathematics等期刊编委。主要从事图论、组合、组合矩阵论、图论在化学和生物学中的应用等方面的研究。2007年-2008年在中田纳西州立大学荣获卓越出版奖；2006年-2007年在中田纳西州立大学荣获杰出科研奖励；2003年-2004年在中田纳西州立大学荣获杰出研究员奖。

报告摘要：Let A be an Abelian group. It is known that an A-connected graph cannot be very sparse. We 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.

It is also known that there are Z_5-connected graph that are not Z_6-connected. We 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 A with order at least 4.