The rainbow connection number of 2-connected graphs

The rainbow connection number of a graph GG is the least number of colours in a (not necessarily proper) edge-colouring of GG such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with nn vertices is at most ⌈n/2⌉⌈n/2⌉. The bound is optimal.