[1] **viXra:1101.0095 [pdf]**
*submitted on 28 Jan 2011*

**Authors:** Yilun Shang

**Comments:** 5 pages

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 connected. Similarly, a vertex-colored graph G is rainbow
vertex-connected if any two vertices are connected by a path whose internal vertices
have distinct colors. The rainbow vertex-connection of a connected graph G, denoted
by rvc(G), is the smallest number of colors that are needed in order to make G rainbow
vertex-connected. We prove that both rc(G) and rvc(G) have sharp concentration in
classical random graph model G(n, p).

**Category:** Combinatorics and Graph Theory