The rainbow connection of a graph is (at most) reciprocal to its minimum degree

@article{Krivelevich2010TheRC,
title={The rainbow connection of a graph is (at most) reciprocal to its minimum degree},
author={Michael Krivelevich and Raphael Yuster},
journal={Journal of Graph Theory},
year={2010},
volume={63},
pages={185-191}
}

An edge-colored graph G is rainbow edge-connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow edgeconnected. We prove that if G has n vertices and minimum degree δ then rc(G) < 20n/δ. This solves open problems from [5] and [3]. A vertex-colored graph G is rainbow vertex-connected if any two vertices are connected by a path… CONTINUE READING