报告题目：Heavy Cycles in Weighted Graphs and Heterochromatic Cycles in Colored Graphs

报告人：张胜贵教授，西北工业大学

报告时间：2014年11月21日15：30—16：30

报告地点：离散数学研究中心学术报告室

报告摘要：

A simple graph is called a weighted graph if each of its edges is associated with a nonnegative number, called the weight of the edge. The weight of a subgraph of a weighted graph is defined as the sum of the weights of its edges. The weighted degree of a vertex is defined as the sum of weights of the edges incident with it. In this talk, we will first give an overview of the results which give weighted degree conditions for the existence of heavy cycles (cycles with large weights) in weighted graphs. These results generalize or extend classical ones on the existences of long cycles in (unweighted) graphs. At the same time, we propose some related problems.

A colored graph is a simple graph in which every edge is associated with a color. The color number of a graph is the number of colors associated with the edges of the graph. The color degree of a vertex in a colored graph is defined as the number colors of the edges incident with it. A cycle is called rainbow if all of its edges have different colors. In this talk, we will introduce some new results on the existence of rainbow cycles of length 3 or 4 under the color number and color degree condition. Our results confirm a conjecture of Li et al. on the existence of rainbow triangles in colored graphs. We also propose some related problems.

报告人简介：张胜贵教授1990年获陕西师范大学基础数学专业学士学位，1993年获西北工业大学应用数学专业硕士学位，2002年获荷兰Twente大学应用数学专业博士学位，2004年破格晋升为西北工业大学教授，2007年任应用数学专业博士生导师。10余次去荷兰、日本、意大利、丹麦和香港等国家和地区的大学进行合作研究和学术交流。现在担任中国组合数学与图论学会理事和中国运筹学会图论组合专业委员会委员。在《Journal of Graph Theory》、《Networks》、《Discrete Mathematics》、《Discrete Applied Mathematics》、《Graphs and Combinatorics》等国内外多种学术期刊上发表论文50余篇，其中30多篇次被SCI和EI检索。3次主持完成国家自然科学基金项目，并多次主持完成省部级基金项目。主持的主要科研项目有“赋权图中的重圈与重割”、“基于图的粘连度和边粘连度的网络抗毁性研究”、“最小权2连通生成子图问题的多项式可解情形”、“图的一些新的连通性参数研究”、“赋权图中的圈”和“拓扑网络树图形生成系统”。

应用研究的主要内容包括：潜通路分析、设施系统的可靠性与抗毁性和图论在生物信息学中的应用。先后主持国家自然科学基金项目4项，部级科研项目2项、国家重点实验室开放课题1项、横向课题1项。