Rainbow connection in $3$-connected graphs

Abstract

An edge-colored graph $G$ is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper, we proved that $rc(G)\le 3(n+1)/5$ for all $3$-connected graphs.

7 pages

Cited by in corpus (2)

• Rainbow Connection Number of Graph Power and Graph Products
• On Rainbow Connection Number and Connectivity