图的b-边染色数及b-边连续性研究

On the b-edge chromatic number and b-edge continuity of graphs

图染色及色数问题是图论中的一个重要内容,也是图论中的一个十分活跃的领域,同时有着深刻而丰富的理论结果和广泛的实际应用,其理论和方法在离散数学中占有重要地位.本文在图的b-染色数和b-连续概念的基础上提出图的b-边染色数及b-边连续的概念,给出了路图、圈图以及满n叉树图的b-边染色数,并且证明了这些图都是b-边连续的.

As an important and animated field of the graph theory,the issue of graph coloring and chromatic number has very profound and plentiful theoretical result and extensive practical application,and its theory and method play an important role in discrete mathematics.In this paper,the concepts of b-edge chromatic number and b-edge continuity are proposed on the basis of the concepts of b-chromatic number and b-continuity.The b-edge chromatic number of the path graph,circle graph and fully n-ary tree graph is given,and the b-edge continuity of these graphs is proved.