Rainbow connection number of graphs with diameter 3
Xueliang Li, Hengzhe Li, Yuefang Sun · Discussiones Mathematicae Graph Theory · 2016
A path in an edge-colored graph G is 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 pair of distinct vertices of G is connected by a rainbow path. Let f (d) denote the minimum number such that rc(G) f (d) for each bridgeless graph G with diameter d. In this paper, we shall show that 7 f (3) 9.