Oriented diameter and rainbow connection number of a graph
Oriented diameter and rainbow connection number of a graph
复制标题
DOI：
10.46298/dmtcs.2093
复制
发表时间：
2011-11
期刊：
影响因子：
--
通讯作者：
Xiaolong Huang;Hengzhe Li;Xueliang Li;Yuefang Sun
中科院分区：
文献类型：
--
作者：
Xiaolong Huang;Hengzhe Li;Xueliang Li;Yuefang Sun
无桥图G的定向直径为min diam(H) | H是G的一个奇异定向。在有边的图G中，相邻的边可能具有相同的颜色，如果没有两条边的颜色相同，则该路径称为彩虹。G的彩虹连接数rc(G)是最小的整数k，使得G存在k边着色，使得G的每两个不同的顶点通过彩虹路径连接。本文用rad(G)和η(G)给出了图的定向直径和彩虹连接数的上界，其中rad(G)是G的半径，η(G)是最小的整数，使得G的每条边都包含在一个长度最多为η(G)的循环中。我们还用G的最小度给出了二部图G的定向直径和彩虹连接数的常界。
The oriented diameter of a bridgeless graph G is min diam(H) | H is a strang orientation of G. A path in an edge-colored graph G, where adjacent edges may have the same color, is called rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer number k for which there exists a k-edge-coloring of G such that every two distinct vertices of G are connected by a rainbow path. In this paper, we obtain upper bounds for the oriented diameter and the rainbow connection number of a graph in terms of rad(G) and η(G), where rad(G) is the radius of G and η(G) is the smallest integer number such that every edge of G is contained in a cycle of length at most η(G). We also obtain constant bounds of the oriented diameter and the rainbow connection number for a (bipartite) graph G in terms of the minimum degree of G.