Approximating layout problems on random graphs

We show that, with overwhelming probability, several well known layout problems are approximable within a constant for random graphs drawn from the G(n, pn) model where C/n ≤ pn ≤ 1 for all n big enough and for some properly characterized parameter C > 1. In fact, our results establish that, with overwhelming probability, the cost of any arbitrary layout of such a random graph is within a constant of the optimal cost.