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The rainbow vertex-connection number, rvc(G), of a connected graph G is the minimum number of colors needed to color its vertices such that every pair of vertices is connected by at least one path whose internal vertices have distinct colors. In this paper we prove that for a 2-connected graph G of order n, rvc(G)≤{⌈n/2⌉−2if n=3,5,9⌈n/2⌉−1if n=4,6,7,8,10,11,12,13 or 15⌈n/2⌉if n≥16 or n=14....
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