【摘要】 有向图的弧色数指的是对有向图的弧进行着色,使得所有连贯弧着不同颜色所需要的最少颜色数.在介绍了一些相关结果的基础上,通过确定顶点数较少的竞赛图弧色数的最大值,说明了已有弧色数的上界虽然对一般有向图是紧的,对竞赛图却是可以改进的.更多还原

【Abstract】 The arc-chromatic number of a digraph is the smallest number of colors required in an arc-coloring such that no two consecutive arcs get the same color.We first introduce some results on the arc-coloring of digraphs,then give a discussion about the upper bound of the arc-chromatic number of tournaments.By determining the maximum arc-chromatic number of tournaments with order at most 8,we show that although the upper bound of the arc-chromatic number of general digraphs is tight,it is not tight for tournaments.更多还原