2011/11/15 by Xiaolong Huang, Huang, Xiaolong, Hengzhe Li +5 · 1 citation
Computer Science · Mathematics · #05C15 #05C40 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1111.3480
openalex publication_date 2011/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The oriented diameter of a bridgeless graph G is min\diam(H) | H is an 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 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.