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
Highly Influential
This paper has highly influenced a number of papers. REVIEW HIGHLY INFLUENTIAL CITATIONS