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西北工业大学张胜贵教授报告会

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    2014年11月21日,西北工业大学张胜贵教授为中心师生作题为“Heavy Cycles in Weighted Graphs and Heterochromatic  Cycles in Colored Graphs”的学术报告。

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.