Dear all,

I encountered a new problem recently about two-connected graphs, of course there was no solution mentioned there. I've been thinking about it some days and could n't solve it. Any body has an idea? Here is the question:

Let G be a two-connected graph. Prove that its vertices can be numbered as v1, v2, . . ., vn in such a way that for all i = 1, 2, . . ., n, both sets {v1, v2, . . ., vi} and

{vi , vi+1, . . ., vn} induce connected graphs.